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Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

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BuyFindarrow_forward

Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

Finding and Checking an Integral In Exercises 69-74, (a) integrate to find F as a function of x, and (b) demonstrate the Second Fundamental Theorem of Calculus by differentiating the result in part (a).

F ( x ) = 8 x t 3 d t

(a)

To determine

To calculate: The value of F(x)=8xt3dt as a function x.

Explanation

Given:

The function, F(x)=8xt3dt

Formula used:

The integration will be broken to parts according to

abf(x)dx=[g(x)]ab.

Also, xndx=xn+1n+1.

Calculation:

The function is integrated within the limits as follows:

F(x)=8xt3dt=8x

(b)

To determine

To calculate: The value of function on differentiation, F(x)=3x43412

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