#### To determine

**To find:** The amount of oil that leaks out during the first hour.

#### Answer

4511.9 Litre per hour

#### Explanation

**Given:** Oil ruptures at t=0 and leaks at the rate of r(t)=100e−0.01tlitres per minute

**Formula used:** ∫abf(x)=−∫baf(x)

r(t)=100e−0.01t=∫060100e−0.01tdt=100∫060e−0.01tdt

Take u=−0.01t

du=−0.01dt=−1100dtm−100du=dt

Where t=0 , u=0t=60 , u=−35

Use the formula ∫abf(x)=−∫baf(x)

Therefore,

=100∫0−35(−100eudu)=100∫−350(100eudu)=10000[eu]−350=10000[e0−e−35]

=10000[1−e−35]=10000[.451188]≈4511.9Litre per hour

**Conclusion:** Hence, oil leaks out during the first hour is 4511.9 Litre per hour.