   Chapter 5, Problem 48RE ### 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 47–50, sketch the region whose area is represented by the definite integral. Then use a geometric formula to evaluate the integral. ∫ 0 6 x 2 d x

To determine

To graph: The region whose area represent by definite integral 06x2dx and calculate integration by use of geometrical formula.

Explanation

Given Information:

The provided definite integral is 06x2dx.

Graph:

Consider the integration,

06x2dx

The integrand function f(x)=x2

Let x=0,

Substitute, 0 for x in f(x)=x2.

f(0)=02=0

Let x=6,

Substitute, 6 for x in f(x)=x2.

f(6)=62=3

The following table represent coordinate of f(x)=x2.

 Coordinate of x Coordinate of y Coordinate of (x,y) 0 0 (0,0) 6 3 (6,3)

The limits of integration from 0 to 6 and integrand x2 is an triangle with base 6 units and height 3 units

The region form by limits and integration is given by

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