# The oil leakage during the first hour. ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805 ### Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

#### Solutions

Chapter 5.5, Problem 63E
To determine

## To calculate: The oil leakage during the first hour.

Expert Solution

Theoil leakage during the first hour is 4,511.88liters_.

### Explanation of Solution

Given:

The function is r(t)=100e0.01t.

Calculation:

The integral function is,R(t)=060r(t)dt.

Substitute (100e0.01t) for r(t).

R(t)=060(100e0.01t)dt (1)

The region lies between t=0 and t=60.

Let u=0.01t (2)

Differentiate both sides of the Equation (2).

du=0.01dtdt=10.01du

Substitute 0 for t in Equation (2) and obtain the lower limit of u.

u=0.01(0)=0

Substitute 60 for t in Equation (2) and obtain the upper limit of u.

u=0.01(60)=0.6

Express the given integral in terms of u.

Substitute u for (0.01t) and (10.01du) for dt in Equation (1).

060(100e0.01t)dt=00.6100eu(10.01du)=1000.0100.6eudu=10,00000.6eudu (3)

Integrate Equation (3).

10,00000.6eudu=10,000[eu]00.6=10,000(e0.6e0)=10,000(0.54881)=4,511.88

Hence, the oil leakage during the first hour is 4,511.88liters_.

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