   Chapter 13, Problem 6RE ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Find the area between the graph of y = x 3 − 4 x + 5 and the x-axis from x =   1  to  x =   3 .

To determine

To calculate: The area under the graph of y=x34x+5 from x=1 to x=3 using the definite integral method.

Explanation

Given Information:

The provided function is y=x34x+5 from x=1 to x=3.

Formula Used:

The sum of n numbers x1, x2, x3,,xn is given by

k=1nxk=x1+x2++xn

The area is given as:

Area=abf(x)=F(b)F(a)

Calculation:

The provided function is y=x34x+5 from x=1 to x=3,

The area obtained is as follows:

Write the expression in the form of limits:

13(x34x+5)dx

Integrate the expression as follows as per the power rule:

Area=13(x34x+5)dx=13x3dx+13(4x)dx+135dx=

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