   Chapter 5, Problem 10RQ ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. ∫ − 5 5 ( a x 2 + b x + c )   d x = 2 ∫ 0 5 ( a x 2 + c )   d x

To determine

To find: Whether the integral relation 55(ax2+bx+c)dx=205(ax2+c)dx is true or false.

Explanation

Given:

The integral relation is 55(ax2+bx+c)dx=205(ax2+c)dx (1)

The region lies between x=5 and x=5.

Theorem used:

1) If f(x)=f(x), that is the equation of the curve is unchanged when x is replaced by x, then the function is an even function and the curve is symmetric about y-axis.

2) If f(x)=f(x), that is the equation of the curve is changed when x is replaced by x, then the function is an odd function and the curve is symmetric about the origin.

Calculation:

Rearrange the left hand side part of equation (1) as shown below,

55(ax2+bx+c)dx=55(ax2+c)dx+55(bx)dx (2)

Consider the integral 55(bx)dx (3)

The function f(x) from equation (3) is,

f(

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