Indefinite Integration Questions and Answers

Question Find the price demand equation for a particular brand of toothpaste at a supermarket chain when the demand is 36 tubes per week at 1 65 per tube given that the marginal price demand function p x for x number of tubes per week is given as p x 0 02e 0 04x If the supermarket chain sells 70 tubes per week what price should be set Round to the nearest cent Provide your answer below

Evaluate the indefinite integral given below e 20 Provide your answer below S e 2 csc 2x 2 csc 2x cot 2x csc 2x dx wwwww 2 csc 2x cot 2x csc 2x dx

Evaluate the indefinite integral given below S sin x 3 sin x sin x 4 sin x cos x dx Provide your answer below f sin x 3 sin x sin x 4 sin x cos x dx 4

Evaluate the indefinite integral given below Provide your answer below 8 36x sec 3x 2x tan 3x 2x dx 8 36x sec 3x 2x tan 3x 2x dx

Consider the function f x 12 Graph the exponential function by hand 0 5 4 Identity any asymptotes 300 250 200 150 100 300 250 200 150 100k 50

Find f f t 4 cost sec t 2 t 2 f 3 3

Find f Use C for the constant of the first antiderivative and D for the constant of the second antiderivative f x 25 6

Find f Use C for the constant of the first antiderivative and D for the constant of the second antiderivative f x 24x 15x 8x f x

1 Given a function of g x on 2 6 and g x 0 on 2 1 g x dx 10 g x 0 on 1 4 g x dx 4 g x 20 on 4 61 g x dx 6 estimate the following integrals 3 points each L g x dx D S Ig x dx A B 6 6 g x dx C lg x g x dx Ef g x dx E

Evaluate the indefinite integral given below using the indicated substitution 8x x 5x x dx u 5x8 x5 Provide your answer below CL

Evaluate the indefinite integral given below using the indicated substitution 2x 2x Provide your answer below 2x 4 dx u 2x 4

The questions in Level 1 are introductory problems The hints contain links to videos covering this content A Question 1 1 point Retake question Which of the following Type 1 Improper Integrals CONVERGE Select all that apply Ste 1 2 da dx 2 X Of 5 1 da of To 27 1 3 of a x dx da x sin x dx

Use a graphing utility to find the point of intersection if any of the graphs of the functions Round your result to three decimal places Enter NONE in any unused answer blanks x y y 110e0 01x y 13 500 x

Question 5 20 points 5 Find the moment of inertia in terms of its mass of a right circular cone of radius r and height h with respect to its axis h Axis

The weekly marginal revenue from the sale of x pairs of tennis shoes is given by the equation below where R x is revenue in dollar 300 x 1 R x 36 0 03x R 0 0 Find the revenue function Find the revenue from the sale of 1 000 pairs of shoes Find the revenue function R x R x Use integers or decimals for any numbers in the expression Find the revenue from the sale of 1 000 pairs of shoes The revenue the sale of 1 000 pairs of shoes is Round to the nearest cent as needed

The marginal average cost of producing x digital sports watches is given by the function C x where C x is the average cost in dollars c x 1 700 2 C 100 27 Find the average cost function and the cost function What are the fixed costs The average cost function is C x The cost function is C x The fixed costs are

The weekly marginal revenue from the sale of x pairs of tennis shoes is given by the equation below where R x is revenue in dollar 400 x 1 Find the revenue function Find the revenue from the sale of 1 000 pairs of shoes R x 30 0 02x R 0 0 Find the revenue function R x R x Use integers or decimals for any numbers in the expression

If tan 0 and sin 0 0 then find a sin 0 b cos 0 c sec 0 d csc 0 e cot 0 FI PI A A

A company determines that its marginal revenue per day is given by R t where R t is the total accumulated revenue in dollars on the fth day The company s marginal cost per day is given by C t where C t is the total accumulated cost in dollars on the fth day R t 130e R 0 0 C t 130 0 6t C 0 0 a Find the total profit P T from t 0 to t 10 the first 10 days P T R T C T R t C t dt The total profit is Round to the nearest cent as needed b Find the average daily profit for the first 10 days The average daily profit is Round to the nearest cent as needed

A company determines that its marginal revenue per day is given by R t where R t is the total accumulated revenue in dollars on the th day The company s marginal cost per day is given by C where C t is the total accumulated cost in dollars on the fth day R t 130e R 0 0 C t 130 0 6t C 0 0 a Find the total profit P T from t 0 to t 10 the first 10 days STIR P T R T C T R t C t dt The total profit is Round to the nearest cent as needed b Find the average daily profit for the first 10 days The average daily profit is Round to the nearest cent as needed GUL

Find the area between the curve and the x axis over the indicated interval y 16 x 4 4 The grounder the sun is Simplify your onewor

Problem 4 By making an appropriate substitution which of the following integrals is equal to SFR Problem 4 dx x x 9 5 2 8 A 37 sin 8 G Select de B 37 sin e cos 8 38 sin 8 de H de c f cos 8 37 sinf 8 de cos 0 37 sin 0 de D 38 sin 6 de E S de F cos 0 37 sin 8 cos 8 38 sin 8 S

Problem 2 By making an appropriate substitution which of the following integrals is equal to tan x sec 0 x dx Problem 2 A u 1 u du B x 1 u du C us 1 u 6 du D u 1 u du E u 1 u du F u 1 u 4 du G u 1 u 5 du H u 1 u du hs Select

A company models its income in thousands of dollars using the conti f t 20e 0 0251 12 where t is measured in months Which of the following denotes the correct formula to find the total income derived in the second year Select the correct answer below 24 O TI 20e 0 0251 1 2 dt 12 TI 2 20e 0 025r 2 dr 20e 0 025t dt O TI 36 O TI 2 20e 0 025z 2 dt O

y 3 M al JS Secti al ah Sketch the region enclosed by the given curves Decide whether to integrate with respect to x or y Draw a typical approximating rectangle y ex y x 1 x 1 x 1 y 3 5 2 0 webassign net y 3 y MacBook Air

2 1 1 M W Sketch the region enclosed by the given curves Decide whether to integrate with respect to x or y Draw a typical approximating rectangle 2x y 8 x y 4 4 al JS Secti 2 1 al WebAssign Plot ah 1 2

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin Foci 7 0 major axis of length 18

Consider the concentration C in mg litre of a drug in the blood as a function of the amount of drug injected x in mg and the time since injection t in hours For 0 x 4 mg and t 0 hours we have C f x t 26xte 4 Calculate the following f 3 4 0 00003511 Give a practical interpretation of your answer Choose the best option f 3 4 is A the amount of a 4 mg dose in the blood 3 hours before injection B the change in concentration of a 4 mg dose in the blood 3 hours after injection C the concentration in the blood 4 hours after injection of a 3 mg dose D the half life of a 3 mg dose in the blood 4 hours after injection E the concentration in the blood 3 hours after injection of a 4 mg dose O F the change in concentration of a 3 mg dose in the blood 4 hours after injection

5 Use the Variations on the Substitution Method to calculate the following integral 2 points 3x 4 hint set u S x sin 3x 4 dx

kf x dx kf f x dx a x g x dx a x dx g x dx f x dx 0 f x dx f x dx a q qf f x g x f x dx g x dx cl cut suck

Monthly sales of a particular personal computer are expected to decline at the following rate of S t computers per month where t is time in months and S t is the number of computers sold each month 2 S t 35t The company plans to stop manufacturing this computer when monthly sales reach 500 computers If monthly sales now t 0 are 1 760 computers find S t How long will the company continue to manufacture this computer S t

Test for exactness If exact solve If not find an integrating factor and solve Find the general and particular soluton 4 y m dx 5 x n dy 0 with initial condition y m n Where m 4 and n 0

roblem 5 Find an integral which represents the volume of the solid obtained by rotating the region enclosed by the curves y x and y 2x 8 about the x axis Problem 5 4 7 x 2x 8 dx B S E 7 x 2x 8 H 7 x4 2x 8 dx 2 B 2x 8 x dx C 7 x 2x 8 dx 76 TU 4 n 2x 8 x G 2x 8 x dx 2 4 4 2x 8 x dx

dx 2 pts each x 1 A Use substitution Hint set u X 1 Su 1 de julidt I tre cit 24 U 25u de jare 3 20 13 Use Integration by Pants Hint setung POL FOL 1 and der Jx17 16 21 du x 7 9 3 2017 26 77 55147 2 50 7 03 225271 4 2 1 x 1 3 du dr chi chu I 2 x 7 c show answer A is the same as conser A 2 x 1 x 1 Wolfie X 2 5 1 2 x 1 da X 2 x 1 2 x 1 t d t X2 x 1 2 dt dx x 2 5 1 2x2 t X 2 x 7 2 x 2 147 FT 3 2x x 1 H 1 x y 2 x 7 4 2 1266 te 3 f

chus In xedx Hint setu x dv ex x 2 pts

Find the derivative of the function y sin sin sin x y

K A 30 m long chain hangs vertically from a cylinder attached to a winch Assume there is no friction in the system and that the chain has a density of 6 kg m Use 9 8 m s for the acceleration due to gravity a How much work is required to wind the entire chain onto the cylinder using the winch b How much work is required to wind the chain onto the cylinder if a 25 kg block is attached to the end of the chain a Set up the integral that gives the work required to wind the entire chain onto the cylinder using the winch Use increasing limits of integration 30 7 9 8 y dy Type exact answers

K Evaluate the following integral 6 9 0 1 3 log 6

K Evaluate the following integral Sx 6 x 6x x

Evaluate the following integral 2 81z 25 dz 2 1 dz dz 81z 25

A commercial cherry grower estimates from past records that if 23 trees are planted per acre then each tree will yield an average of 37 pounds of cherries per season If for each additional tree planted per acre up to 23 additional trees the average yield per tree is reduced by 1 pound how many trees should be planted per acre to obtain the maximum yield per acre What is the maximum yield In order to get the highest yield of pounds trees should be planted per acre

State two other forms for the line integral J F T ds given that F f g h SF T OA Srdx gdy hdz and f F r t dr C OB 1 dx gdy h dz and 1 df g dg h dh C C OC SF dr and OD F dr and F r t dr C F dr and f df g dg h din dh C C

Determine the indefinite integral S 6 16 x dx S 6 16 x dx Check the answer by differentiation

Evaluate the following integral 3 fx 8x dx

K Find the derivative of the following function and evaluate the derivative at the given value of x f In 8x f x 8x f x x e 8 X In 8x 1 In 8x 8 In 8x In x In 8 Simplify your answer CED

K Evaluate the following integral dx x 11 x 0 dxa Question 21 7

Evaluate the following integral 5 dx 4x 54 dx 4x 5 In 5

y x 45 dy dx Type an exact answer using radicals as needed N

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are measured in meters Assume the water level is at the top of the dam termine the total force on the dam Lengths Oc w y 5 y OD w y 5y OA JO Lo EEXEED Set up the integral that should be used to find the total force on the face of the dam Use increasing limits of integration Select the correct choice below and fill in the answer b complete your choice Type exact answers dx CO 20 16