APPLICATION I. Find the antiderivatives of the following functions using the substituion rule. Write your answers on a separate sheet of paper. a. S(5x + 4)*dx c. S sin"(x) cos(x) dx d. (-de
APPLICATION I. Find the antiderivatives of the following functions using the substituion rule. Write your answers on a separate sheet of paper. a. S(5x + 4)*dx c. S sin"(x) cos(x) dx d. (-de
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![APPLICATION
I. Find the antiderivatives of the following functions using the substitufion rule. Write
your answers on a separate sheet of paper.
b. Váx - 5dx
d. fdx
a. S(5x + 4)*dx
c. S sin"(x) cos(x) dx
II. Find and correct the mistakes in the following "solutions" to these integration
problems. Write the new solutions in the space provided below.
a. ( sin 5x dx u Sx, du = Sdr
sin Sx dx =
sin u du = - cos u +C = -S cos 5x +C
9
cas
dx;u = sin1, du = cosI dr
1+sin'"
b.
du
= In|1 + u+C = In| 1 + sim지 + C
cos I
-dx 3D
+ sinx
:xp:
c. [(4x + 1)(2x +x)i dx;u = 2r +1, du = 4x +1
*+ 1)(2x* + xy* dx = [ uñdu =(2r* + x)* +c](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe363552c-6088-4d64-aea5-d6bce20115e6%2Ff9af907e-8b86-4243-833b-53ba356a3d7e%2Fr6i0eg8_processed.png&w=3840&q=75)
Transcribed Image Text:APPLICATION
I. Find the antiderivatives of the following functions using the substitufion rule. Write
your answers on a separate sheet of paper.
b. Váx - 5dx
d. fdx
a. S(5x + 4)*dx
c. S sin"(x) cos(x) dx
II. Find and correct the mistakes in the following "solutions" to these integration
problems. Write the new solutions in the space provided below.
a. ( sin 5x dx u Sx, du = Sdr
sin Sx dx =
sin u du = - cos u +C = -S cos 5x +C
9
cas
dx;u = sin1, du = cosI dr
1+sin'"
b.
du
= In|1 + u+C = In| 1 + sim지 + C
cos I
-dx 3D
+ sinx
:xp:
c. [(4x + 1)(2x +x)i dx;u = 2r +1, du = 4x +1
*+ 1)(2x* + xy* dx = [ uñdu =(2r* + x)* +c
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