1. Find the antiderivatives of the following functions using the substitution rule. Write your answers on a separate sheet of paper. a. (5x+4) dx b./√x-5dx c. f sin¹(x) cos(x) dx d. fdx
1. Find the antiderivatives of the following functions using the substitution rule. Write your answers on a separate sheet of paper. a. (5x+4) dx b./√x-5dx c. f sin¹(x) cos(x) dx d. fdx
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![APPLICATION
1. Find the antiderivatives of the following functions using the substitution rule. Write
your answers on a separate sheet of paper.
a. [(5x + 4)5dx
b. √ √4x-5dx
c. sin¹0 (x) cos(x) dx
d. fdx
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= 5x, du = 5dx
sin 5x dx =
= [₁ sin u du = -cos u + C = -5 cos 5x + C
9
cost_dx;Mm. sản x, du = cosx dx
1+ an
cos x
du
-dx =
1+ SIR²X
1+u²
c. f(4x + 1)(2x² + x) dx;u= 2x² + x, du = 4x + 1
[(4x + 1
x +
b.
= In||1 + u²| + C = In|1+ sin³x|+C
1)(2x² + x) dx = [uħdu = ²(2x²+x) + C](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe363552c-6088-4d64-aea5-d6bce20115e6%2Fa972ee13-8525-4b90-8160-ac424c51d674%2Fvvapyqh_processed.png&w=3840&q=75)
Transcribed Image Text:APPLICATION
1. Find the antiderivatives of the following functions using the substitution rule. Write
your answers on a separate sheet of paper.
a. [(5x + 4)5dx
b. √ √4x-5dx
c. sin¹0 (x) cos(x) dx
d. fdx
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= 5x, du = 5dx
sin 5x dx =
= [₁ sin u du = -cos u + C = -5 cos 5x + C
9
cost_dx;Mm. sản x, du = cosx dx
1+ an
cos x
du
-dx =
1+ SIR²X
1+u²
c. f(4x + 1)(2x² + x) dx;u= 2x² + x, du = 4x + 1
[(4x + 1
x +
b.
= In||1 + u²| + C = In|1+ sin³x|+C
1)(2x² + x) dx = [uħdu = ²(2x²+x) + C
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