Indefinite Integration Questions and Answers

Use substitution to find the indefinite integral Sp p 5 dp 18

Evaluate the definite integral 6 3 3x 1 dx

Use integration by parts to find the integral x 5 In x dx AX Inx x 5x C OA O B Inx x C OC Inx C 12

Find the indefinite integral S4x In 7x dx for x

Use substitution to find the given indefinite integral x 3x 2 dx x 3x x 3x 2 dx

Determine the indefinite integral S 27 x In 4x 27 dx

se substitution to find the indefinite integral 5x e8x dx

Use substitution to find the indefinite integral SPCE p p 9 5 dp 5

se substitution to find the indefinite integral 6x 1 S 3x x 4 dx Describe the most appropriate substitution case and the values of u and du Select the correct choice below and fill in the answer boxe so that du A Substitute u for the quantity in the numerator Let u B Substitute u for the entire quantity in the denominator Let u C Substitute u for the quantity raised to an integer power Let u dx so that du dx so that du dx

Evaluate the integral 6e6t S 6 e6t 6e6t dt C

se substitution to find the given indefinite integral 2 k dk 3k 2e

4 Use the Fourier transform to solve the following differentia equation if Fly jwf y y 3y 6u t e 3t Bu t e t 38 t

1 25 points Evaluate lim x 0 xf sin 1 dt X sin x4 2 25 points If f x f where g x cos z 1 sin t dt find 3 25 points Evaluate 4 2x x 1 x 1 S dx 4 25 points Use the method of disks to determine the volume of the solid obtained by rotating th region bounded by y 2x and y x about the x axis

Suppose that f x 7x 6 and g x 3x 4 a Solve f x 0 b Solve f x 0 d Solve f x g x c Solve f x g x e Graph y f x and y g x and find the point that represents the solution to the equation f x g x

Evaluate the indefinite integral 3e 3e sin e dr UL Davidan M Message instru ctol

Evaluate the definite integral 1 4e in cos 1 dr

Evaluate the indefinite integral N t 4 Question Helni 2 Joibruisu 3Bassan AEPA

The value of dr is Question Help Video Message Calculator Submit Question FERME

Evaluate the indefinite integral 8 sin 2 o 8 sin 1 cos 1 dr E FINRU Message instructor

Evaluate the integral by interpreting it in terms of areas In other words draw a picture of the region the integral represents and find the area using geometry S 3x 10 dx Question Help Video Message instructor

2 The following integral can be computed using trigonometric substitution Identify what number is playing the role of alpha and write down the appropriate substitution to compute this integral Again don t actually evaluate the integral 81 x dx

The following integral can be computed using integration by parts Identify what would play the ra of u and dv From this find du and v Don t actually evaluate the integral S x 5x sin 3x dx

Find a cosine equation having the following characteristics Amplitude 2 Period 2 Horizontal Shift 2TT Vertical Shift 6 y cos x Enter

Give the complex number of point A yi B 6 5 4 3 a 327 2 1 7 6 5 4 3 2 11 2 D 3 4 5 6 7 J A 1 2 3 4 5 6

3 Evaluate the following integrals and state which case number from the lecture 3 notes each integral falls under a cos r sin zda Hint COS I cos x b sin Hint Case 3 from lecture 3 notes c sin zdr sin r rcos zdr d sin r cos Hint This is both case 3 and case 4 from lecture 3 notes Either method will work e cos4 cos rdx xdx Hint This is case 5 from lecture 3 notes Look at the last example of the lecture 3 notes to see how to start this question Keep in mind that there will be a cos 2x term appearing To deal with this you must use the identity once again cos 2 r 1 cos 4 Notice that the input of cosine gets doubled when the identity is applied 2 f cos r s cos r sin rdr

Use the table to find f 3 X 2 1 O 1 3 5 9 f 3 f x 1 2 1 9 5 O 3

W SHEET NION LOW CALORIE SWEETENER po

4 Solve for y y 1 y6 xy5 where y 1 1

2 Find f x of f x 2 xusing the definition Find the equation of the tanger line to the graph of the function at 9 6

e integrand in the problem da can be re written as a product like this 2 dx apply integration by parts we can let u x and dv en du 1dx and v arctan hat are the next steps for trying the integration by parts technique here 1 z 1 2 dr uv fv du z arctan z 1 de arctanz r C uv fv du z arctanz farctan z dz Stop here and try a different approach because we don t have a good way to antidifferentiate arct

c Determine the exact value of x 5 n 5 Hint First find the Mclaurin series for e

Evaluate the indefinite integral arcsin x Narcsin 1 a arcsin 9 9 da X

Evaluate the integral by making the appropriate substitution u T da 6x 12 da 6x 12

Compute the given integral 1 da H

Question 12 Evaluate the indefinite integral 25

Use a Table of Integrals to evaluate the integral fesz sin 6zdz

Graph the following rational functions Put the solutions a f x x 1 x 9x b f x 2 9

Which of the following graphs is the slope field for O 17 11 3 2 1 3 TI 711 2 1 dx x T O 1 3 2 3 2 111 2 3 4 5 6 7 8

Score 11 12 answerec Question 6 re cosu If d z 4 42 9 du then

Evaluate the indefinite integral 52 2 x 1 dr

Find Vf at the given point f x y z x y 3z z In x 1 2 5 Vfl 1 2 5 i k Type exact answers using radicals as needed

8 Evaluate f 1 dx Option A c A 5 MMA m 10 295 3 0 B B5 8 C B 0 C 5 8 C PVP D

13 hind the integral A cy 2 dx option A 4 in 1x1 2x MD 97 B 8 2 20 C 1 C 4in x1 2extc 0 2x c 0 28 XZ C

Find f 3 x 7 dx Question Help Video Message instru Calculator

Evaluate the definite integral K24 sin 2t dt

6 n f x 5 dz 5 Question Help OVideo Message instruct Calculator

For each table below select whether the table represents a function that is increasing or decreasing and whether the function is concave up or concave down I f x 1 2 3 4 5 6 f x is Select an answer Select an answer I g x 7123 4 5 6 456 2 8 18 32 50 72 H 1 2 3 4 72 5 6 50 g x is Select an answer Select an answer I h 1 1 198 2 192 3 182 168 150 128 32 18 8 2 h r is Select an answer k z 128 150 168 182 192 198 Select an answer k z is Select an answer Select an answer 4

Evaluate the indefinite integral 2x 1 pa da x 1 C

1 Evaluate the following integrals using integration by parts Clearly denote what is playing the role of u du du and v a in zdr Hint The integral is equivalent to In a 1dx b in Hint Set u In r as in the integration by parts formula Use your answer from part a c farctan Hint Use the same hint from part a d a cos x dx Hint Rewrite the integrand as r r cos x Now experiment as to what to set u and du equal to Do not use online resources nrdr ctan x dx

Compute the given integral 1 7 x 36 dx