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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Chapter
Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Use Property 8 to estimate the value of the integral.

0 1 x 3 d x

To determine

To calculate: The value of the integral function 01x3dx.

Explanation

The integral function is 01x3dx (1)

Consider the function f(x)=x3 (2)

The region lies between x=0 and x=1.

Apply Property 8 of integrals:

If mf(x)M for axb, then m(ba)abf(x)dxM(ba).

Calculate the absolute maximum value using Equation (2).

M=f(x) (3)

Substitute 1 for x in Equation (3).

M=f(1)=(1)3

Calculate the absolute minimum value using Equation (2)

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