   Chapter 13.2, Problem 41E ### 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 curve y =   − x 2 +   3 x   −   2 and the x-axis from x   =   1  to  x   =   2 .

To determine

To calculate: The area between the curve y=x2+3x2 and the x-axis from x=1 to x=2.

Explanation

Given Information:

The provided curve is y=x2+3x2 and the range of x-axis is from x=1 to x=2.

Formula used:

The area under a curve from a to b is the absolute value of the definite integral of the function calculated with the lower limit a and upper limit b.

To calculate a definite integral, evaluate the indefinite integral and then substitute the limits of the integral.

The value of the integral xndx=xn+1n+1.

Calculation:

The provided curve is y=x2+3x2 and the range of x-axis is from x=1 to x=2.

Thus, the upper limit for x is 2 and the lower limit is 1.

Recall that area under a curve from a to b is the absolute value of the definite integral of the function calculated with the lower limit a and upper limit b.

Thus, the area between the curve and the x-axis is given by the integral 12(x2+3x2)dx.

Use the formula xndx=xn+1n+1 to evaluate the integral.

12(x2+3x2)dx=(x2+12+1+3x1+11+12x)12=(x

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