Indefinite Integration Questions and Answers
![Evaluate the integral xex 11 x 11 dx Xe dx](https://media.kunduz.com/media/sug-question-candidate/20230422165006570263-4364004.jpg?w=256)
![K Decide whether each of the pairs of angle right are alternate interior angles same s alternate exterior angles 21 and 26 22 and 23 24 and 25 Choose the statement that correctly des](https://media.kunduz.com/media/sug-question-candidate/20230422161028841678-3653173.jpg?w=256)
Calculus
Indefinite IntegrationK Decide whether each of the pairs of angle right are alternate interior angles same s alternate exterior angles 21 and 26 22 and 23 24 and 25 Choose the statement that correctly des
![n 17 of 21 1 point Attempt 1 of Unlimited View qu omplex numbers z and Z2 2 2i 2 10 10i exact answer in reduced fraction form if neces 0 2 of 2](https://media.kunduz.com/media/sug-question-candidate/20230422150621242944-4537299.jpg?w=256)
Calculus
Indefinite Integrationn 17 of 21 1 point Attempt 1 of Unlimited View qu omplex numbers z and Z2 2 2i 2 10 10i exact answer in reduced fraction form if neces 0 2 of 2
![1 Question 9 of 10 Solve the equation Writ log4 5q 11 1](https://media.kunduz.com/media/sug-question-candidate/20230422105503381848-5366129.jpg?w=256)
![Find an antiderivative of the following function by trial and error Check your answer by differentiation e8x 3 Se x 3 dx 8 X Teleg](https://media.kunduz.com/media/sug-question-candidate/20230422033945758219-4486849.jpg?w=256)
Calculus
Indefinite IntegrationFind an antiderivative of the following function by trial and error Check your answer by differentiation e8x 3 Se x 3 dx 8 X Teleg
![Use the substitution u x 2 to evaluate the indefinite integral below 2x x 2 dx Write the integrand in terms of u S2x x 2 dx du Evaluate the integral 2x x 2 dx](https://media.kunduz.com/media/sug-question-candidate/20230422033248796878-4486849.jpg?w=256)
Calculus
Indefinite IntegrationUse the substitution u x 2 to evaluate the indefinite integral below 2x x 2 dx Write the integrand in terms of u S2x x 2 dx du Evaluate the integral 2x x 2 dx
![Consider the following function Step 2 of 2 Find the length of the individual line segments of this function Then find the positive vertical separation between each line segment Simplify your ans](https://media.kunduz.com/media/sug-question-candidate/20230422005611827047-5506401.jpg?w=256)
Calculus
Indefinite IntegrationConsider the following function Step 2 of 2 Find the length of the individual line segments of this function Then find the positive vertical separation between each line segment Simplify your ans
![2 pts Indefinite integrals Is the following equation True False Give a short justification 3x Sav dx x 1 C where C is the integration constant 2 x 1](https://media.kunduz.com/media/sug-question-candidate/20230422001058297479-3636637.jpg?w=256)
Calculus
Indefinite Integration2 pts Indefinite integrals Is the following equation True False Give a short justification 3x Sav dx x 1 C where C is the integration constant 2 x 1
![5 2 pts u substitution Find the indefinite integral cos 0 de using the u substitution u sin 0 Hint cos 0 1 sin 0](https://media.kunduz.com/media/sug-question-candidate/20230422001212692087-3636637.jpg?w=256)
Calculus
Indefinite Integration5 2 pts u substitution Find the indefinite integral cos 0 de using the u substitution u sin 0 Hint cos 0 1 sin 0
![ose the correct answer below A 19 C B 15 C C 40 C](https://media.kunduz.com/media/sug-question-candidate/20230421160421697407-3653173.jpg?w=256)
![Find the volume of the solid obtained by rotating about the x axis the region enclosed by the curves y 25 x 25 y 0 x 0 and x 5](https://media.kunduz.com/media/sug-question-candidate/20230421030430655386-4641188.jpg?w=256)
Calculus
Indefinite IntegrationFind the volume of the solid obtained by rotating about the x axis the region enclosed by the curves y 25 x 25 y 0 x 0 and x 5
![5 Consider two complex variables w u iv and z x iy and the map given by w 2 For contours u constant in the w plane draw the contours to which they map in the 2 plane Repeat for contours constant in the w plane Show that the two sets of contours in the z plane are orthogonal to each other That is just as the contours for u constant and constant are perpendicular to each other everywhere they intersect so for the corresponding contours in the z plane For this reason we refer to this mapping function as a conformal map Conformal maps have many applications in science and engineering](https://media.kunduz.com/media/sug-question-candidate/20230421003944733967-5548229.jpg?w=256)
Calculus
Indefinite Integration5 Consider two complex variables w u iv and z x iy and the map given by w 2 For contours u constant in the w plane draw the contours to which they map in the 2 plane Repeat for contours constant in the w plane Show that the two sets of contours in the z plane are orthogonal to each other That is just as the contours for u constant and constant are perpendicular to each other everywhere they intersect so for the corresponding contours in the z plane For this reason we refer to this mapping function as a conformal map Conformal maps have many applications in science and engineering
![3 17 x 0 7 x 17 x dx 1 x 7 x 5](https://media.kunduz.com/media/sug-question-candidate/20230420190122831684-4646611.jpg?w=256)
![6 Rewrite the integral integration dx dy dz f x y z dz dy dx as an iterated integral with order of](https://media.kunduz.com/media/sug-question-candidate/20230420053144462988-5548868.jpg?w=256)
Calculus
Indefinite Integration6 Rewrite the integral integration dx dy dz f x y z dz dy dx as an iterated integral with order of
![Find the area of the region R that lies under the given curve y f x over the indicated interv a x b 3 Under y 7 2x over 21 x 1 O 12 O 12 O 3 35 5 3 5 35](https://media.kunduz.com/media/sug-question-candidate/20230420005030821376-4090272.jpg?w=256)
Calculus
Indefinite IntegrationFind the area of the region R that lies under the given curve y f x over the indicated interv a x b 3 Under y 7 2x over 21 x 1 O 12 O 12 O 3 35 5 3 5 35
![estion 3 2 x 2 K 3 3x and f 1 16 then f x](https://media.kunduz.com/media/sug-question-candidate/20230419164545348797-5061986.jpg?w=256)
![Given that the graph of f x passes through the point 4 2 and that the slope of its tangent line at x f x is 3x 5 wha f 3](https://media.kunduz.com/media/sug-question-candidate/20230419043750191113-5502565.jpg?w=256)
Calculus
Indefinite IntegrationGiven that the graph of f x passes through the point 4 2 and that the slope of its tangent line at x f x is 3x 5 wha f 3
![Find the general antiderivative for dx dt 5t 3](https://media.kunduz.com/media/sug-question-candidate/20230419044355758824-5502565.jpg?w=256)
![Consider the function f x whose second derivative is f x 5x 4 sin x If f 0 2 and f 0 4 what is f x f x](https://media.kunduz.com/media/sug-question-candidate/20230419043712876690-5502565.jpg?w=256)
Calculus
Indefinite IntegrationConsider the function f x whose second derivative is f x 5x 4 sin x If f 0 2 and f 0 4 what is f x f x
![Find the most general antiderivative for the function Antiderivative 4 Vx 5 x 1](https://media.kunduz.com/media/sug-question-candidate/20230419032914768937-5502565.jpg?w=256)
Calculus
Indefinite IntegrationFind the most general antiderivative for the function Antiderivative 4 Vx 5 x 1
![Let f x I 6e Enter an antiderivative of f x](https://media.kunduz.com/media/sug-question-candidate/20230419032555372640-5502565.jpg?w=256)
![Find an antiderivative for the function 8 6xe x](https://media.kunduz.com/media/sug-question-candidate/20230419032952350069-5502565.jpg?w=256)
![Find the general antiderivative for y C dy da 3e](https://media.kunduz.com/media/sug-question-candidate/20230419032403830591-5502565.jpg?w=256)
![13 1 x Let f x Enter an antiderivative of f x r](https://media.kunduz.com/media/sug-question-candidate/20230419032818874345-5502565.jpg?w=256)
![Find the most general antiderivative for the function Note Don t enter the C It s included for you Antiderivative 4 u](https://media.kunduz.com/media/sug-question-candidate/20230419032523490283-5502565.jpg?w=256)
Calculus
Indefinite IntegrationFind the most general antiderivative for the function Note Don t enter the C It s included for you Antiderivative 4 u
![Consider the function f x 12x 27x2 20x 9 Enter an antiderivative of f x](https://media.kunduz.com/media/sug-question-candidate/20230419032505451726-5502565.jpg?w=256)
Calculus
Indefinite IntegrationConsider the function f x 12x 27x2 20x 9 Enter an antiderivative of f x
![Consider the function f x 6x 2x 5 on 0 9 The absolute maximum of f x on 0 9 is at x on 0 9 is The absolute minimum of f x on 0 9 is at x 0 9 is and the absolute maximum of f x and the absolute minimum of f x on](https://media.kunduz.com/media/sug-question-candidate/20230418174913367159-5452618.jpg?w=256)
Calculus
Indefinite IntegrationConsider the function f x 6x 2x 5 on 0 9 The absolute maximum of f x on 0 9 is at x on 0 9 is The absolute minimum of f x on 0 9 is at x 0 9 is and the absolute maximum of f x and the absolute minimum of f x on
![The slope f x at each point x y on a curve y f x is given along with a particular point a b on the curve Use this information to find f x f x ex x7 0 9 f x e x O 8 f x ex 10 8 8 18 f x e x 10 8 f x e x 16 8](https://media.kunduz.com/media/sug-question-candidate/20230418175219823503-4090272.jpg?w=256)
Calculus
Indefinite IntegrationThe slope f x at each point x y on a curve y f x is given along with a particular point a b on the curve Use this information to find f x f x ex x7 0 9 f x e x O 8 f x ex 10 8 8 18 f x e x 10 8 f x e x 16 8
![Evaluate 5 Set 4 et dt 5 Se dt et 4 F Type an exact ansv](https://media.kunduz.com/media/sug-question-candidate/20230418044547664444-3967093.jpg?w=256)
![Use basic integration formulas to compute the following antiderivatives or definite integrals 7 12 de x 207 e 12 2 2 dz 2x 208 I da 2x 209 12 210 x 1 22 dx](https://media.kunduz.com/media/sug-question-candidate/20230418032300635271-4565383.jpg?w=256)
Calculus
Indefinite IntegrationUse basic integration formulas to compute the following antiderivatives or definite integrals 7 12 de x 207 e 12 2 2 dz 2x 208 I da 2x 209 12 210 x 1 22 dx
![Evaluate Assume x 0 Check by differentiating x 5 In x dx x 5 In x dr](https://media.kunduz.com/media/sug-question-candidate/20230418031707005021-3967093.jpg?w=256)
![Evaluate Assume x 0 Check by differentiating fx ll x In x dx x In x dx](https://media.kunduz.com/media/sug-question-candidate/20230418031644211562-3967093.jpg?w=256)
Calculus
Indefinite IntegrationEvaluate Assume x 0 Check by differentiating fx ll x In x dx x In x dx
![Evaluate the integral using integration by parts Sxe 10x dx x 10x dx](https://media.kunduz.com/media/sug-question-candidate/20230418031732295789-3967093.jpg?w=256)
![Find f such that f x 2x 5x 8 and f 0 6 f x](https://media.kunduz.com/media/sug-question-candidate/20230418030128930347-3967093.jpg?w=256)
![Evaluate the definite integral by interpreting it in terms of areas 3x 12 dx](https://media.kunduz.com/media/sug-question-candidate/20230418013603590722-5502565.jpg?w=256)
Calculus
Indefinite IntegrationEvaluate the definite integral by interpreting it in terms of areas 3x 12 dx
![Evaluate the given indefinite integrals 3 sin x da a b 18 sec s ds C C 7 sec t tan t 19 csc t cot t dt C](https://media.kunduz.com/media/sug-question-candidate/20230417210551501200-4971328.jpg?w=256)
Calculus
Indefinite IntegrationEvaluate the given indefinite integrals 3 sin x da a b 18 sec s ds C C 7 sec t tan t 19 csc t cot t dt C
![Evaluate the given indefinite integrals a dy b 17 5 5 u duz u7 4 c 321 C 8x4 dx C C C](https://media.kunduz.com/media/sug-question-candidate/20230417210534360324-4971328.jpg?w=256)
Calculus
Indefinite IntegrationEvaluate the given indefinite integrals a dy b 17 5 5 u duz u7 4 c 321 C 8x4 dx C C C
![Evaluate the given indefinite integrals d a 1dr b 20 dys S717 C dz C C C](https://media.kunduz.com/media/sug-question-candidate/20230417210515077504-4971328.jpg?w=256)
Calculus
Indefinite IntegrationEvaluate the given indefinite integrals d a 1dr b 20 dys S717 C dz C C C
![Suppose that f x dx 5 and the following exercises compute the integrals 88 89 x 9 x d 90 9 2 9 x dx S f x 9 x dx 91 S 92 f x 9 x dx 2 3 S f x dx 3 and 9 2 da 1 and 9 2 dx 2 In 3f x 4g x dx](https://media.kunduz.com/media/sug-question-candidate/20230417161115995930-4565383.jpg?w=256)
Calculus
Indefinite IntegrationSuppose that f x dx 5 and the following exercises compute the integrals 88 89 x 9 x d 90 9 2 9 x dx S f x 9 x dx 91 S 92 f x 9 x dx 2 3 S f x dx 3 and 9 2 da 1 and 9 2 dx 2 In 3f x 4g x dx
![the following exercises compute the integrals Suppose that 88 f x g x da 89 f x dx 5 and 1 f a da 3 and f x g x da 1 9 x dx 2 In 9 x dx 1 and](https://media.kunduz.com/media/sug-question-candidate/20230417072757020674-4565383.jpg?w=256)
Calculus
Indefinite Integrationthe following exercises compute the integrals Suppose that 88 f x g x da 89 f x dx 5 and 1 f a da 3 and f x g x da 1 9 x dx 2 In 9 x dx 1 and
![15 A women invests 6200 in an account that 60 interest per year compounded continuously A What is the amount after 3 years pays Round your answer to the neartest cent B How long will it take for the amount to be 10 000 answer to two decimal places Round your](https://media.kunduz.com/media/sug-question-candidate/20230416203643445497-4787741.jpg?w=256)
Calculus
Indefinite Integration15 A women invests 6200 in an account that 60 interest per year compounded continuously A What is the amount after 3 years pays Round your answer to the neartest cent B How long will it take for the amount to be 10 000 answer to two decimal places Round your
![Find the time it takes for 10 000 t compounded continuously years Find the time it takes for 1 000 00](https://media.kunduz.com/media/sug-question-candidate/20230416192739458445-4453710.jpg?w=256)
Calculus
Indefinite IntegrationFind the time it takes for 10 000 t compounded continuously years Find the time it takes for 1 000 00
![Approximate the area under the graph of f x 8x 7 from x 2 to x 4 a Use left endpoints b Use right endpoints](https://media.kunduz.com/media/sug-question-candidate/20230416152625213080-5422331.jpg?w=256)
Calculus
Indefinite IntegrationApproximate the area under the graph of f x 8x 7 from x 2 to x 4 a Use left endpoints b Use right endpoints
![3 Evaluate fff xyz dV where T is the tetrahedron with vertices 0 0 0 1 0 0 1 1 0 1 0 1](https://media.kunduz.com/media/sug-question-candidate/20230416081102012494-5538341.jpg?w=256)
Calculus
Indefinite Integration3 Evaluate fff xyz dV where T is the tetrahedron with vertices 0 0 0 1 0 0 1 1 0 1 0 1
![Use substitution techniques and a table of integrals to find the indefinite integral x x6 9dx Click the icon to view a brief table of integrals Choose the most useful substitution below OA u x O B u x3 O c u x OD u x 9 6 OE u x 9 ww](https://media.kunduz.com/media/sug-question-candidate/20230416013222086232-4364004.jpg?w=256)
Calculus
Indefinite IntegrationUse substitution techniques and a table of integrals to find the indefinite integral x x6 9dx Click the icon to view a brief table of integrals Choose the most useful substitution below OA u x O B u x3 O c u x OD u x 9 6 OE u x 9 ww
![If you want to use integration by parts to find x 1 x 5 dx which is the better choice for u u x 1 6 or u x 5 Explain your choice then integrate Choose the correct answer below www OA The better choice is u x 5 because it is next to dx in the integrand OB The better choice is u x 1 because it contains a quantity to a power OC The better choice i e is u x 1 6 because it is easier to integrate Su dv C D The better choice is u x 5 because it is easier to integrate Ju dv](https://media.kunduz.com/media/sug-question-candidate/20230415222831174089-4364004.jpg?w=256)
Calculus
Indefinite IntegrationIf you want to use integration by parts to find x 1 x 5 dx which is the better choice for u u x 1 6 or u x 5 Explain your choice then integrate Choose the correct answer below www OA The better choice is u x 5 because it is next to dx in the integrand OB The better choice is u x 1 because it contains a quantity to a power OC The better choice i e is u x 1 6 because it is easier to integrate Su dv C D The better choice is u x 5 because it is easier to integrate Ju dv
![The integral can be found in more than one way First use integration by parts then expand the expression and integrate the resu 8x 9 x 2 dx Identify u and dv when integrating this expression using integration by parts](https://media.kunduz.com/media/sug-question-candidate/20230415195242639751-4364004.jpg?w=256)
Calculus
Indefinite IntegrationThe integral can be found in more than one way First use integration by parts then expand the expression and integrate the resu 8x 9 x 2 dx Identify u and dv when integrating this expression using integration by parts
![Integrate as indicated Sx ex ax dx 7x 7 x et](https://media.kunduz.com/media/sug-question-candidate/20230415194158623896-4364004.jpg?w=256)
![Integrate by parts Assume x 0 x Inx dx x In x dx](https://media.kunduz.com/media/sug-question-candidate/20230415193922477006-4364004.jpg?w=256)
![The marginal cost of manufacturing x yards of a certain fabric is C x 3 0 01x 0 000006x2 in dollars per yard Find the increase in cost if the production level is raised from 2000 yards to 4000 yards](https://media.kunduz.com/media/sug-question-candidate/20230415042717435153-4075097.jpg?w=256)
Calculus
Indefinite IntegrationThe marginal cost of manufacturing x yards of a certain fabric is C x 3 0 01x 0 000006x2 in dollars per yard Find the increase in cost if the production level is raised from 2000 yards to 4000 yards