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Problem 53 Medium Difficulty

If oil leaks from a tank at a rate of $ r(t) $ gallons per minute at time $ t $, what does $ \displaystyle \int^{120}_0 r(t) \, dt $ represent?

Name: if oil leaks from a tank at a rate of rt gallons per minute at time t what does displaystyle int120_
Uploaded: 2019-12-04
Duration: 43 s
Channel: Numerade
Description: If oil leaks from a tank at a rate of $ r(t) $ gallons per minute at time $ t $, what does $ \displaystyle \int^{120}_0 r(t) \, dt $ represent?

Answer

$$V(0)-V(120)$$

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Video Transcript

okay if the FT is the volume of the tank than our tea is the derivative of Viotti Soviet prime of tea. So what this means is that the integral from 01 20 r t G t is equivalent to this integral from 0 to 1 20 off the prime of tea. Because remember their equivalent. I just rode out the equivalent statement right over there. But fundamental dilemma calculus part to this is vey of 1 20 minus V of zero. In other words, bound the first found months, the second round. So what this means is that this represents the change in volume of the tank from th zero toe Tia's 1 20 which is the amount of oil leaked in the 1st 2 hours because they're 60 minutes in an hour.

Amrita B.

Topics

Integrals

Integration

Calculus: Early Transcendentals

Chapter 5