Chapter 13.2, Problem 57E

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11th Edition

Ronald J. Harshbarger + 1 other

ISBN: 9781305108042

Textbook Problem

** Total income** The income from an oil change service chain can be considered as flowing continuously at an annual rate given by

Find the total income for this chain over the first 2 years (from

).

To determine

**To calculate:** The total income for the oil change service chain over the first 2 years where the income is given by

Explanation

**Given Information:**

The provided function is

**Formula used:**

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

The value of the integral *a* is constant and *x* is variable.

**Calculation:**

Consider the function

Since, total income from

Thus, total income is

Since,

Thus, the integral is

Recall that to calculate a definite integral, evaluate the indefinite integral and then substitute the limits of the integral.

Thus, evaluate the integral.

Consider the expression

Differentiate with respect to *t*.

Thus,

Simplify the integral by the use of

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