Indefinite Integration Questions and Answers

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

WOWWW

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

Use a change of variables to evaluate the following definite integral 2 9 27v 9 9 0 27v 9 S dv dv Type an exact answer using radicals as needed

Evaluate the following integral 2x 2x 2x 2x 1 dx dx

Evaluate the integral 10tedt 101 dt

Evaluate the following integral 11x e x 5 dx e x 5 dx 11x

Evaluate the following integral Include absolute values only when needed dx 9x 7 Sa dx 9x 7 9 on 10 7 2 42 In 9x 7

K Find the mass of the thin bar with the given density function 3x 4 p x 1 sinx for 0 sxs Set up the integral that gives the mass of the thin bar 3x 4 S 1 sinx dx 0 Type exact answers The mass of the thin bar is Type an exact answer units

Let R be the region bounded by y x x 1 and y 0 Use the shell method to find the volume of the solid generated when R is revolved about the line y 3 Set up the integral that gives the volume of the solid using the shell method Use increasing limits of integration Select the correct choice below and fill in the answer boxes to complete your choice Type exact answers O A O B TO dy LE Jod dx

1 8x2 1 2x x 1 d da

Using synthetic division determine whether the numbers are zeros of the polynomial function 4 2 1 h x x 3x 2x 4x 8 Is 2 a zero of h x x 3x 2x 4x 8 No OYes Is 1 a zero of h x x 3x 2x 4x 8 No Yes

Last month Kaitlin s average daily balance on her credit card was 1 340 71 The annual interest rate on that credit card is r charge 1 B 365 17 71 The minimum payment on that card is the interest n plus 2 of the ending balance or 25 which ever is larger If there were 30 days in that month and the ending balance was 1 946 54 what would be the minimum payment that Kaitlin could make Round your answer to the nearest penny Input the number Do not input the dollar sign Do not use a comma Example 89 65

Given the function f find the slope of the line tangent to the graph of f1 at the specified point on the graph of f f x x 4 for x2 4 16 0 The slope of the line tangent to the graph of f at 16 0 is Simplify your answer 1

6 1 X f x f x 2 3 2 a f 4 b f 1 c f 3 d f 3 3 4 13 05 3 7 3 lo 6 8 OA 4 Type an integer or a fraction OB 4 cannot be determined or state that the derivative cannot be determined 2 MA a Choose the correct answer below and if necessary fill in the answer box within your choice

Find the inverse of the one to one function State the domain and the range of the inverse function 10 15 9 11 8 14 7 13 6 15 The inverse function is Type an ordered pair Use a comma to separate answers as needed

Find the degree measure of each angle without using a calculator Check your answers using a graphing calculator a 11 3 660 b 4 720 c 2 1 14159 X

Evaluate the integral by interpreting it in terms of areas x 2 dx

Evaluate the integral by interpreting it in terms of areas dx

Determine whether the sequence associated with the series is arithmetic or geometric n 2 2 n 0 arithmetic O geometric Find the common difference or ratio Find the sum of the first 15 terms

Write the first five terms of the geometric sequence Find the common ratior and write the nth term of the sequence as a function of n 16 1 31 a a3 34 a5 r S 11

Suppose 15000 is invested at 8 interest compounded continuously How long will it take for the investment to grow to 30000 Use the model A t Pert and round your answer to the nearest hundredth of a year years for the investment to reach 30000 It will take

Find the mass of the thin bar with the given density function p x x x 14 x 2 for 0 x 3 The mass of the thin bar is Type an exact answer units

The gravity on the moon is known to be constant at approximately 1 62 m s Suppose while on the moon a rock is thrown such that after 1 second its velocity is 12 m s and its height is 17 m above the moon s surface Using concepts and notation from calculus a Determine the position function of the rock s t b Determine the maximum height of the rock

A spring on a horizontal surface can be stretched and held 0 5 m from its equilibrium position with a force of 65 N a How much work is done in stretching the spring 2 5 m from its equilibrium position b How much work is done in compressing the spring 3 5 m from its equilibrium position a Set up the integral that gives the work done in stretching the spring 2 5 m from its equilibrium position Use increasing limits of integration dx www Type exact answers

Use a change of variables or the table to evaluate the following indefinite integral 8 Sx x 1 d dx Click the icon to view the table of general integration formulas 8 x x 1 dx

Find the mass of the thin bar with the given density function p x 4 if 0 x 3 4 x if 3 x 5 m units Simplify your answer Type an integer or a decimal

11 Consider a cylindrical tank that has a height of 11 m and a radius of 4 m Recall that if the tank is full of water then S 16mpg 15 y dy equals the work required to pump all the water out 0 of the tank through an outflow pipe that is 15 m above the bottom of the tank Revise this work integral for the following scenario Do not evaluate the integrals The work required to empty the tank through an outflow pipe at the top of the tank If D y is the distance a horizontal slice must be lifted what is D y when the outflow pipe is at the top of the tank D y

Why must integration be used to find the work required to pump water out of a tank OA Integration is necessary because the acceleration of gravity changes at each level B Integration is necessary because W mgy O C Water from the same horizontal planes is lifted different distances D Different volumes of water are moved different distances

Find the mass of the thin bar with the given density function 3x 4 p x 1 sin x for 0 x Set up the integral that gives the mass of the thin bar dx Type exact answers