Now recall the Simple Power Rule where n ≠ − 1 and C is the constant of integration. Find the indefinite integral. Check your result by differentiating.[ 8x dxStep 1Recall the Constant Multiple Rule where k is a constant and f(x) is a function.dx = k f(x) dxKS F(x[₁For[kf(x)8x dx, we have k = 8 ✔1fxd[8x dx8x dx = 8 ✔Step 2Now recall the Simple Power Rule where n - 1 and C is the constant of integration.[x² dxdx =x + 1n+ 18 and f(x) = x. Applying the Constant Multiple Rule gives the following result.+ CWe note that we can write 88√x dx as 8 / x²xdx as 8 x¹ dx. Therefore, n =and n + 1 =Applying the Simple Power Rule gives the following result. (Use C for the constant of integration.)8/x dx -=

Answered: Image /qna-images/answer/ac6feb5a-8c2c-449e-90ee-e3ab43a6a8fd.jpg

Answered: Find the indefinite integral. Check…

Find the indefinite integral. Check your result by differentiating. Jaxax 8x dx Step 1 Recall the Constant Multiple Rule where k is a constant and f(x) is a function.

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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Question

Now recall the Simple Power Rule where

n ≠ − 1

and C is the constant of integration.

Find the indefinite integral. Check your result by differentiating.
[ 8x dx
Step 1
Recall the Constant Multiple Rule where k is a constant and f(x) is a function.
dx = k f(x) dx
KS F(x
[₁
For
[kf(x)
8x dx, we have k = 8 ✔
1fxd
[8x dx
8x dx = 8 ✔
Step 2
Now recall the Simple Power Rule where n - 1 and C is the constant of integration.
[x² dx
dx =
x + 1
n+ 1
8 and f(x) = x. Applying the Constant Multiple Rule gives the following result.
+ C
We note that we can write 8
8√x dx as 8 / x²
xdx as 8 x¹ dx. Therefore, n =
and n + 1 =
Applying the Simple Power Rule gives the following result. (Use C for the constant of integration.)
8/x dx -
=

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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