The rate at which water is sprayed on a field of vegetables is given by R(t)=2sqrt(1+5t^3), where t is in minutes and R(t) is in gallons per minute. During the time interval 0 to 4 inclusive, what is the average rate of water flow, in gallons per minute?

Question

The rate at which water is sprayed on a field of vegetables is given by R(t)=2sqrt(1+5t^3), where t is in minutes and R(t) is in gallons per minute.  During the time interval 0 to 4 inclusive, what is the average rate of water flow, in gallons per minute?

anonymous · Answer

The formula is 1/b-a int(equation) from zero to four. Just integrate normally and multiply by the first part.

regan · Answer

integrate with limits 0,4 then divide by 4

anonymous · Answer

Ie,
$$1\div4 \int\limits_{0}^{4} 2\sqrt{1+5t ^{3}} dt$$

regan · Answer

nailed it

anonymous · Answer

I got 14.691
What do a & b represent in the average rate equation?

anonymous · Answer

It is the average value theorem.

anonymous · Answer

Essentially, to explain geometrically, it is the same as taking the average of any numbers. You take the sum and then divide by how many numbers you had originally, right? You had a certain amount between b, which is 4, and a, which is 2. That is represented by the integration. You divide by their difference because it is the space between in terms of x, or in this case, t.

Does that answer your question?

anonymous · Answer

Why does a=2

anonymous · Answer

Therefore, the average value theorem states that the average value is simply the integration times 1/b-a

anonymous · Answer

I'm sorry, that was a typo. A is 0.

anonymous · Answer

Ok, thanks