Indefinite Integration Questions and Answers

Evaluate the integral xex 11 x 11 dx Xe dx

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

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

1 Question 9 of 10 Solve the equation Writ log4 5q 11 1

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

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

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

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

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

ose the correct answer below A 19 C B 15 C C 40 C

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

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

3 17 x 0 7 x 17 x dx 1 x 7 x 5

6 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

estion 3 2 x 2 K 3 3x and f 1 16 then f x

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

Find the general antiderivative for dx dt 5t 3

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

Find the most general antiderivative for the function Antiderivative 4 Vx 5 x 1

Let f x I 6e Enter an antiderivative of f x

Find an antiderivative for the function 8 6xe x

Find the general antiderivative for y C dy da 3e

13 1 x Let f x Enter an antiderivative of f x r

Find 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

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

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

Evaluate 5 Set 4 et dt 5 Se dt et 4 F Type an exact ansv

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

Evaluate Assume x 0 Check by differentiating x 5 In x dx x 5 In x dr

Evaluate 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

Find f such that f x 2x 5x 8 and f 0 6 f x

Evaluate 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

Evaluate 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

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

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

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

Find 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

3 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

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

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

Integrate as indicated Sx ex ax dx 7x 7 x et

Integrate by parts Assume x 0 x Inx dx x In x dx

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