Indefinite Integration Questions and Answers

3 Evaluate the following integrals a 10 pts x x 1 e dr

Determine the number of the graph of the function 2h r 6 9 O O N 6 3 O a 1 O b 3 O c 5 5 d 4 IN e 2 9 6 3 3 6 st 6 3 to

Use integration to find f 4 if 5x and f 1 7 dx O 26 667 O 19 667 O 26 667 O 30 333 42 43 44 45 4

What is F x 3 dx o F x 2 In lx 31 3 In 3 F x ln x 3 3 In 3 C o F x 2 lx 31 3 3 C In F x 2 In lx 31 3 3 C In

Use a Table of Integrals to evaluate the integral Jetz sin 4xdx

6x 4x 9x 5 dx 6x 4x 9x 5 dx 6x 4x 9x 5 dx Tyne an exact power

Sketch the region enclosed by the given curves y 10 8 6 2 Y y 16x y x 2 Need Help Find the area of the region 4 Read It 6 Watch It X 0 8 X y 10 8 6 2 1 2 3 4 5 X DO 10 8 6 2 6 8 o y 10 8 1

Find the area of the shaded region A y x 4 2 4 2 y 8 6 4 2 1 6 3y 2x 16 2 4 y 8 2x 2 4 X

Sketch the region enclosed by the given curves y 12 x y x 6 y kkk 6 4 2 5 10 Find the area of the region 2 4 6 X 6 4 2 10 5 2 4 10 4 2 10 2 4 6 6 10

Evaluate the improper integral dx x 1

using substitute for the problem State the meaning of u du and other expressions that you might use as a substitute within a given problem In othe expressions like u and du without writing out what they mean no matter how obvious you think that their meanings are 1 DETAILS LARCALCET7 8 1 017 Find the indefinite integral Use C for the constant of integration 17 z 19 17 dz

Find the indefinite integral using the substitution x 5 tan 0 Use C for the constant of integration 25 x dx

Find the indefinite integral by using the substitution x 2 sec 0 Use C for the constant of integration x x 4 X dx

FIND THE EQUATION OF THE T AND LA TO THE CURVE y sin 2x 7 5 GRAPH THE AT POINT FUNCTION

6x7 4 10x7 3 6x7 4 10 7 4 10x713 dy dx

Total expenditures in a country in billions of dollars are increasing at a rate of f x 9 38x 87 11 where x 0 corresponds to the year 2000 Total expenditures were 1584 88 billion in 2002 a Find a function that gives the total expenditures x years after 2000 b What will total expenditures be in 2013 a What is the function for the total expenditures F x Simplify your answer Use integers or decimals for any numbers in the expression b In 2013 total expenditures will be billion

Evaluate the following indefinite integral 1 11 5 3t 1 11 5 dt

Determine the indefinite integral 2x f7e x dx

If the rate of excretion of a bio chemical compound is given by f t 0 06e 0 06t the total amount excreted by time t in minutes is f t a Find an expression for f t b If 0 units are excreted at time t 0 how many units are excreted in 29 minutes a Find an expression for f t f t

Evaluate fast x tan x dx C

at is f x f 6x 2x 3 dx O F x x x 3x C O F x 2x x 3x C O F x 2x x 3x C F x 2x x 3x

Find the following indefinite integral S 2 2 3e 0 1x dx X 2 X 3e 0 1x dx

etermine the indefinite integral f2e x dx 7x

Find the following indefinite integral 7 dy dy

S 7x 7x 10x 7x 2 dx 7x 10x 7x 2 dx Type an exact answer

Evaluate the following indefinite integral f11dx Curdy

Evaluate the following indefinite integral 18 18x dx

A solid is obtained by rotating the shaded region about the specified line about the x axis y V 4 3 2 1 y x 2 4 2TY y 6 x 6 8 i a Set up an integral using the method of cylindrical shells for the volume of the solid dy X b Evaluate the integral to find the volume of the solid 10

Evaluate the indefinite integral cot x csc x dx

Racing cars driven by Chris and Kelly are side by side at the start of a race The table shows the velocities of each car in miles per hour during the first ten seconds of the race VcVK t 0 0 1 2 3 4 5 0 t VC 6 68 VK 61 69 79 21 22 7 74 85 31 35 8 81 93 47 53 9 86 98 54 60 10 91 103 Use the midpoint rule to estimate how much farther in mi Kelly travels than Chris does during the first ten seconds Round your answer to four decimal places

Sketch the region enclosed by the given curves y sec x y 8 cos x X 5 1 0 0 5 0 1 5 1 0 0 5 y y the region 44x 0 5 1 0 16 0 5 1 0 1 5 1 5 1 0 0 5 8 6 0 5 1 0 1 5 1 5 1 0 0 5 2 8 0 5 1 0 1 5 X

Set up an integral for the area of the shaded region Evaluate the integral to find the area of the shaded region x y 6 3 y 2 2 3 y 1 x e 2 y 1 4

is the part of the cone z 6 x y above the z 0 plane are integral equals 2 y 42 ds

Decide whether the integral is improper 8 sin x 57 x 00 O proper O improper dx Explain your reasoning Select all that apply The limits of integration are both finite The integrand is continuous on The integrand is not continuous on 0 At least one of the limits of integration is not finite

What is F x o F x O F x o F x O F x dx 5x In lxl ln x C In Ixl C ln x

if dx x x 3 which of the following statements is true of dx x 3 is the only solution for the antiderivative x 3 is the general solution for the antiderivative 1 x 3 dx of dx x 3 is the particular solution for the antigerivative of dx 1 2 3 4 5 6

Finally recall the following theorem 1 If r 0 is a rational humber then lim 0 x xx Applying this gives us the following 8 7 lim 818 5 lim X18 3 lim X48 1 8 7 1 5 0 3 C Therefore evaluating the given limit gives the following result If the limit is infinite enter o or as appropriate If the limit does not otherwise exist enter DNE 8x 7 lim x 5x x3

Find f Find f x cos x f 0 5 f 0 1 f 0 6

Evaluate the integral fz 2 4 dz by making the substitution u C NOTE Your answer should be in terms of I and Question Help Video Message instructor

In a batch of 21 pedometers 3 are believed to be defective A quality control engineer randomly selects 6 units to test Let random variable X the number of defective units that are among the 6 units tested a Find the probability mass function f x P X x and sketch its histogram b Find P X 1 What does this number represent c Find P X 1 What does this number represent Using the hypergeometric probability distribution model set up an expression that can be used to find a single ordered pair in the probability mass function f x P X x QB 8 a Find the probability mass function f x P X x f x P X x SOA f x Type an ordered pair Use a comma to separate answers as needed Round to five decimal places as needed Let x the number of defective pedometers among the 6 units tested and let y f x Choose the correct histogram below AY 0 7 0 67 0 5 nA Simplify your answers Q O B Ay 0 7 0 6 0 54 04 Q O C AY 0 7 0 6 0 54 ni Q O D AY Submit quiz 0 74 0 6 0 5

Find 16 4x 2 dr 2 dz Question Help Video Mes Calculsor

4 Evaluate the following integrals by method of trigonometric substitution and state which case number from the lecture 4 notes each integral falls under a b ITA Hint c Hint I da x x 4 sec Cos tan 0 sin 0 x dx tan 0 sec 9 dx sin 20 cos 0 Now perform a simple u sub to integrate sec 0 1 sec sec 0 cos 0

If a population of is becoming extinct and the population is decaying exponentially Assume that there are 2 000 animals and there will only be one animal in 50 years What is k the rate of decay N

Compute the given integral ftan ada

Evaluate the indefinite integral 6dr I ln 91

Evaluate the indefinite integral 2 6 z dz Question Help Ovideo Message ins

Which function represents y tan x A 1 4 B D TT

2 Let n be a fixed positive integer Use integration by parts to prove the following reduction formula x e dx 1 2 n T 1e dr Note The formula is called a reduction formula because the exponent of the term has

Graph the parabola y 2x 16x 29 Plot five points on the parabola the vertex two points to the left of the vertex and two points to the right of the vertex Then click on the graph a func button Tv 12 10 84 198 X D L

Rewrite the following equation with the variables separated y Z 7 2x o 7dy y 7 xdx ody 7xdx y 7 o y 7 dy 7xdx 77 78 79 80 81 82 83