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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Find the most general antiderivative of the function. (Check your answer by differentiation.)

f ( x ) = x 2 3 + x x

To determine

To find: The most general antiderivative of the function f(x)=x23+xx and check the determined antiderivative for the function f(x)=x23+xx by differentiation.

Explanation

Given Data:

Write the given function as follows.

f(x)=x23+xx

Formula used 1:

The antiderivative function for the function xn is xn+1n+1+C .

Here, C is the constant.

Formula used 2:

Write the required differentiation formula to verify the answer as follows.

ddx(xn)=nxn1ddx(constant)=0

Calculation:

Rewrite the function f(x)=x23+xx as follows.

f(x)=x23+x1(x12)

f(x)=x23+x32 (1)

From the antiderivative function formula, the antiderivative function for the function in equation (1) is written as follows.

F(x)=x23+123+1+x32+132+1+C=x5353+x5252+C=35x53+25x52+C

Thus, the most general antiderivative of the function f(x)=x23+xx is 35x53+25x52+C_ .

Here, the determined antiderivative for the function f(x)=x23+xx is 35x53+25x52+C

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