Application of integration, Change in volume

[dbag]

Hello

Problem statement:
Container hold 200 Liters of water, when we begin to empty the container the amount of water going out is 16-0.8t liters/minute, where t is time in minutes. Calculate how much water gets out in 20 minutes

Solution:
Taking a definite integral between 0 and 20 gets me a 16t-0.4t², then plugging 20 in place of t i get an answer of 160 liters, so during 20 minutes 160 liters of water leaves the container. Is this correct?
Thanks

 

[Dr.Peterson]

Yes, that's correct.

As a check, observe that the rate is initially 16, and ends up at 0 liters per minute, so the average is 8. That times 20 minutes is 160 liters. (This trick works only for linear functions.) Also, it's good that we still have water left.

 

[dbag]

thank you very much

Yes, that's correct.

As a check, observe that the rate is initially 16, and ends up at 0 liters per minute, so the average is 8. That times 20 minutes is 160 liters. (This trick works only for linear functions.) Also, it's good that we still have water left.