   Chapter 5.4, Problem 4E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Evaluating a Definite integral using a Geometric Formula In Exercises 1–6, sketch the region whose area is represented by the definite integral. Then use a geometric formula to evaluate the integral. See Example 1. ∫ 0 3 x 3 d x

To determine

To graph: The definite integral 03x3dx and calculate its area using geometric formula.

Explanation

Given Information:

The provided integral is,

03x3dx

Graph:

Consider the integral,

03x3dx

The function is f(x)=x3.

For x=2,

Substitute x=2 in the f(x)=x3 as below,

f(2)=23=0.66667

For x=1,

Substitute x=1 in the f(x)=x3 as below,

f(1)=13=0.333

For x=0,

Substitute x=0 in the f(x)=x3 as below,

f(0)=03=0

For x=1,

Substitute x=1 in the f(x)=x3 as below,

f(1)=13=0

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