Indefinite Integration Questions and Answers

Use partial fractions to find the indefinite integral Remember to use absolute values where appropriate Use C for the constant of integration x 36x 36 x3 4x In x 2 4 x x 2 4 C dx

1 Points Evaluate the indefinite integral Use C for the constant of integration x 8 x dx

Evaluate the indefinite integral Remember to use absolute values where appropriate Use C for the constant of integration t 1 4t 8t 7 log 147 81 71 x Remember to use capital C dt

Use partial fractions to evaluate the definite integral Use a graphing utility to verify your result S In 2 2 3x 4x 1 dx

Use substitution and partial fractions to find the indefinite integral Remember to use absolute values where appropriate Use C for the constant of integration x 2 x 4ln dx D x x 4 4 C

Assume that perimeter of a two dimensional shape is given with function f x OA There is no such OB 4 In x th 3 Ocje Find the value of that gives the largest perimeter ODT O E 1 e t 4 dt Lo x value earctant dt

Let be a finite positive integer If lnx dx 3 then what is the value of the integral S in x 1 da in terms of 3 A 2e k 1 B B e k 1 8 c e k 1 B O Dek k 1 B E 2e k k 1 8

Question 8 Integrate 1 x3 x8 25 dx A C

Evaluate the flux integral ff Fds where F x y z x 1 y 2 3 and C is the outward upward oriented half sphere z 9 x y 0 z 3

Question 12 Evaluate the indefinite integral ST X x 5 C

Question 3 J Find 4x6 2 X 6 x 3 x dx C

tan x 7 tan x 12 Step 2 Rewrite the polynomial in the denominator as u 7u 12 u 4u 1 u 7u 12 where A and B are to be determined U 3 Collect the terms according to the power of u on the right side and factorize u 7u 12 u u 4 3 u 4 u 4 u 3 Because u 7u 12 u 4 u 3 you should include one partial fraction for each factor and write B A U 4 1 U 4 Rey 3 u 12 U Step 3 Multiplying this equation by the least common denominator u u 3 yields the basic equation 3 B u 4 7 7 u 12

et 24 ex 20 dx 5 88 Points DETAILS LARCALCET7 8 5 031 MI Use substitution and partial fractions to find the indefinite integral Remember to use absolute values where appropriate Use C for the constant of integration x

x 4x 1 5 88 Points DETAILS LARCALCET7 8 5 009 Use partial fractions to find the indefinite integral Remember to use absolute values where appropriate Use C for the constant of integration 2x 16x 39x 32 dr

5 x x 1 True False A can be put in the form X B 2 X 1 I where A and B are constants

Graph t rabola y x 6x 4 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 funct button 12 10 By 12 X D 5

Which function matches the indefinite integral dx o F x 12 1 2x O F x C 4x F x C o F x 1 C

Rewrite F x as F u using a substitution of variables F x f 6x 5 4 3x 5x dx o F u f4 du o F u f 4 du o F u f 42u du F u f 4 dx

Which of the following statements match the indefinite integral e dx of e dx C In x of et dx et C of e dx et of e dx e C T 2 3 LG 5 co 6

Consider the function y 4 sin 2x x Give exact answers using fractions and multiples of Determine the following information a Amplitude 4 b Period T c Phase shift Direction Left Number of units enter a positive number using fractions and multiples of d The point 0 0 transformed into e The point 1 transformed into f Graph the function 57 8 2 37 8 7 4 7 8 P 2 10 S 704 3 8 22 S 8 3x T

x 3 dx x What is F x O F x x 3 C O F x x 3 C F x x 3 c C F x x 3

For the slope field shown which could be a family of anti derivatives 3 2 111 O y x C O y x C o y x C oy e C

An object is moving along a horizontal path shown in the graph 5 3 2 2 3 4 5 114 AD What is the displacement of the object for the time interval 2 5 O Displacement is 5 O Displacement is 5 O Displacement cannot be determined from the information given O Displacement is 9

Consider the function y 4 sin 2x Give exact answers using fractions and multiples of Determine the following information a Amplitude 4 b Period c Phase shift Direction Left Number of units enter a positive number using fractions and multiples of T 2 d The point 0 0 transformed into 0 0 e The point f Graph the function 57 8 transformed into 37 8 N 7U4 7 8 718 74 1 2 X Clear All Braw 0 04 X 3782 57 8 37

Find the indefinite integral using the substitution x 6 sin 8 Use C for the constant of integration 1 36 x273 2 dx 1 36 X 36 x 2 C

Find the indefinite integral using the substitution x 10 sec 0 Use C for the constant of integration x 100 dx 3x 200 x 100 15 C

Find the indefinite integral using the substitution x 4 sin 8 Remember to use absolute values where appropriate Use C for the constant of integration 16 x dx 16 x X 16 2 4 C

dx x 9 x 2 True O False 9 2 9x C

Solve the initial value problem for r as a vector function of t d r Differential equation 36k 2 dt posall conce r t Di j k Foppistandsmitaj PRICES Initial conditions r 0 50k and dr dt EMILELENIE Det er OINE t 0 S 2i 2j

For the function f x 5x 8x 7x 2 find f x Then find f 0 and f 4 x

J PREVIOUS ANSWERS Evaluate the indefinite integral Remember to use absolute values where appropriate Use C for the constant of integration dx 4x 5 In 4x 5 C SCALCET9 5 5 015 MI

The concentration C of a chemical in the bloodstream t hours after injection into muscle tissues is given by the following 2t 64 3 C t t20 a Complete the table and use it to approximate the time when the concentration is greatest Round your answers to three decimal places 0 5 1 1 5 2 2 5 3 3 5 t t C t O b Use a graphing utility to graph the concentration function and use the graph to approximate the time when the concentration is the greatest C 3 C B 1 06 1 05 1 04 1 03 1 02 1 01 0 06 0 05 0 04 0 03 hr 0 02 0 01 0 hr 0 0 5 0 5 1 1 15 15 2 1 25 3 2 2 5 3 3 5 3 5 Cit CID 1 02 0 00 0 05 0 02 1 04 1 03 0 04 0 03 0 01 1 06 1 05 0 1 01 O 0 5 1 0 5 1 15 c Use calculus to determine analytically the time when the concentration is greatest 15 2 MY NC 3 5

Evaluate the integral by making the given substitution Use C for the constant of integration xex d dx U x

Evaluate the inde 36 10e da 36 10e In gral 36 10e 36 1 36 100t 20 C

0 0 1 Points DETAILS Find the general indefinite integral Use C for the constant of integration Remember to use absolute values where appropriate 7 dr 81 r 18 log r r C PREVIOUS ANSWERS SCALCET9 5 4 020 Need Help Read It X

Evaluate the indefinite integral 36 10e da

1 Points Find the general indefinite integral Use C for the constant of integration Remember to use absolute values where appropriate 2 dr

d Interpret the integral in part c as a difference of areas O The integral represents the area below the x axis minus the area above the x axis O The integral represents the area above the x axis minus the area below the x axis Illustrate with a diagram 4 3 DU y 6 Help Read It 2 3 3 4 3 10 3

When integrating trigonometric functions if you have an even power on sine or cosine you should use a half angle formula O True False

Evaluate the definite integral 2 cos t dt 50 sin t In 51 ln 50

The graph of a function fis given Estimate 0 1 0 10 f x dx using five subintervals with the following a right endpoints c midpoints b left endpoints

Evaluate the indefinite integral s 7 t 10 6 dt

Find T N and x for the plane curve r t 2t i 2 In cos t j R

v 2 dr Then find the length of the indicated portion of the curve r 1 4cos 11 4 Find the arc length parameter along the given curve from the point where t 0 by evaluating the integral s t j 5t k where Ostsz

Evaluate the integral 120 x 49 r dx

A B Find the exact surface area by rotating the curve about the y axis x t and y 2t 3 1st 1 C D E TC 4 16 3 5 2 2 27 27 13 18 9 13 7 6 T 7 9 3 4 TC 13 13 8 A

1 2 X e 1 e X 1 X 2 x 1 X X 1 dx

x x 21 dx 1 10x x 15 10x x 21 4 x 21 7 69 7 69 Points DETAILS c C 11 arctan x dx PREVIOUS ANSWERS LARCALCET7 8 2 031 Find the indefinite integral Note Solve by the simplest method not all require integration by parts Use C for the constant of integration 1

Find the indefinite integral by using substitution followed by integration by parts Use C for the constant of integration 2 29 sin 29x dx s 29x sin 29x C 2 29x cos 29x cos 29x

Use the tabular method to find the integral Use C for the constant of integration 19x 9x sin x dx 3 9 x cos x 3x sin x 6x cos x 6 sin x C