Indefinite Integration Questions and Answers

Evaluate the indefinite integral 6x sec 2 ta

Evaluate the indefinite integral 3 J 8 x dx V x 0

Find the rational function s asymptotic x intercepts and holes Also sketch the graph of the rational function Then list the domain and range using interval notation Hint x 4 is a difference of two squares a b a b a b f x 3x 6x x 4 7

Find the extremals for f y dx subject to the condition Sydx 3 y 0 1 y 1

Use the given graphs of the function f left in blue and g right in red to find the following limits 1 lim f x g x help limits 2 lim f x g x 3 lim f x g x 2 0 f x z 0 g x 4 lim 5 lim 24 1 3 f x 1 0 qz 3 3

Evaluate the integral 0x 81 sec 0 Ox 9 tan 0 x 9 sin 0 Ox 81 tan 0 Ox 9 sec 0 A Which trig substitution is correct for this integral O x 81 sin 0 282 1 cot 0 81 x dx B Which integral do you obtain after substituting for and simplifying Note to enter type the word theta 1134 sin de C What is the value of the above integral in terms of 0 D What is the value of the original integral in terms of x 1 1 x sin 2 sin x 1 2 4 C C

4xe dx 5x C

im 0 sin x So In 1 t at dt sin x 2

2 In x 2 4 2 X X 1 dx

x 5 S 4 2 2 dx 6 f 3 sin 2x cos 2x dx

8 f 8x dx

6 f cos x 4x5 ln x da

4 f 10 5 dx 22

1 f x sin x e dx

u b c f 2X Fs dx

Problem 30 1 point If f t 7 1 sin t 6 cos t and f 0 5 find f A 128 D 131 C 130 B 129 E 132

Isy 19x a solution of the differential equation dx Explain BOCCOD The function y 19x a solution of the differential equation because when it is substituted into the differential equation side of the equation is equal to and the right side of the equation is equal to Simplify your answers

Find the integral by whatever means are necessary either substitution or tables Remember to use absolute values where appropriate Use C for the constant of integration 1 25 x X dx 25 x In 25 1 5 25 x 5 CX

Find the integral Hint Separate the integral into two integrals using the fact that the numerator is a sum or difference and find the two integrals by two different formulas Remember to use absolute values where appropriate Use C for the constant of integration 1 x 9 x 0 dx

Find the integral by whatever means are necessary either substitution or tables Remember to use absolute values where appropriate Use C for the constant of integration 1 25 X dx X

Find the indefinite integral Use C for the constant of integration Remember to use absolute values where appropriate e av x dx X

Find the indefinite integral Use C for the constant of integration Remember to use absolute values where appropriate 45x 45x2 3x1 30e x dx

December 15 2023 1 Integrate the following expressions a S 5x x 12 dx b S 5x 4x dx odnalgus oils gaivlover vd basera x 2x 2 A ball is rolling down a slope with an acceleration noget up J21 up J2ift ori sins veri 01 10802 Tir 1080251 3w elxs t a 4 2t where t is the time in s Find the bal f time if v 5 m s when t 0 babnued noigeted to abiono s ruod

12 2x 3 c 2 2 2

2x 3 c 2x 2

2x 3 c 2x 2 2

6 r x sin x cos x 2 0 7

72 sin 2x 3 dx A cos 2x 3 C B cos 2x 3 C C cos 2x 3 D cos 2x 3 C 1 E cos 2x 3 C

10 If y is implicitly defined by 4 cos x sin y 1 Then y A 1 4 1 1 sin x cos y bb C 1 4 tan x tan y D E tan r tan u B tan x tan y edmuntadt 50 sin y cos x

You go to the doctor and he gives you 17 milligrams of radioactive dye After 12 minutes 8 milligrams of dye remain in your system To leave the doctor s office you must pass through a radiation detector without sounding the alarm If the detector will sound the alarm if more than 2 milligrams of the dye are in your system how long will your visit to the doctor take assuming you were given the dye as soon as you arrived Give your answer to the nearest minute You will spend minutes at the doctor s office

Find f Jes 2x Cos Cx

Calculate the indicated Riemann sum S4 for the function f x 34 4x Partition 0 12 into four subintervals of equal length and for each subinterval X 1X let c 2xx 1 xx 3 SA Simplify your answer SKELB

15 cos 0 60

14 tan 0 600 y

27 tan 3

2 cos 0 300 riangle 1 uni X

Find the integral by using the integral table on the inside back cover Remember to use absolute values where appropriate Use C for the constant of integration 1 Z 25 2 dz

Find the integral by using the integral table on the inside back cover Remember to use absolute values where appropriate Use C for the constant of integration x 36 dx

Find the integral by using the integral table on the inside back cover Hint Use formula 15 with a 4 Use C for the constant of integration Remember to use absolute values where appropriate 1 x 16 dx

Find the integral by using the integral table on the inside back cover Use C for the constant of integration Remember to us absolute values where appropriate x 1 x 9 dx

Find the area between y 9 and y x 1 with a 0 F TH

Consider the function f t 5 sec t 4t Let F t be the antiderivative of f t with F 0 0 32 Then F 2 5 tan 2 OF

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function tanz S 6t t dt

Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function 5 7 1 t 7 g x Question Help dt Video Message instructor

Find 32 3 Find 3x x 1 dx

3 Find 3x x 1 da

2 Find I cos 0 sin 0 de 10 9 19 slingbaon do pilog off mot sa om my moldog nivellot si to lis od anoitourten evinson 1 1 tl dusze eld amplas haditios I tomusob eids gningiz va ogbolT ala orozite of qlod obivorq ton bib S bus ou widton hib bus avdellve od ni vjes

59 y 3 cos 30 5 3 2 3 60 120 180 240 300 360

Use a graphing calculator to find where the curves intersect and to find the area between the curves y ex y 3x 5x a The left point of intersection is Type integers or decimals rounded to the nearest thousandth as needed Type an ordered pair

Monthly sales of a particular personal computer are expected to decline at a rate of S t 5te lt computers per month where t is time in months and S t is the number of computers sold each month The company plans to stop manufacturing this computer when monthly sales reach 900 computers If monthly sales now t 0 are 2 000 computers find S t How long to the nearest month will the company continue to manufacture the computer S t