Chapter 13.2, Problem 43E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

Find the area between the curve
*x*-axis from *x* = 1 to *x =* 3.

To determine

**To calculate:** The area between the curve *x*-axis from

Explanation

**Given Information:**

The provided curve is *x-* axis is from

**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.

According to the power rule of derivatives:

If *u* is a function of *x*, then

Where *c* is constant.

**Calculation:**

The provided curve is *x-* axis is from

Thus, the upper limit for *x* is 3 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

Consider the expression

Differentiate with respect to *x*.

Thus,

Simplify the integral using

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