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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Section
BuyFindarrow_forward

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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