AP Calculus AB : Definite integral of the rate of change of a quantity over an interval interpreted as the change of the quantity over the interval

Study concepts, example questions & explanations for AP Calculus AB

varsity tutors app store varsity tutors android store

Example Questions

1 3 Next →

Example Question #21 :Definite Integral Of The Rate Of Change Of A Quantity Over An Interval Interpreted As The Change Of The Quantity Over The Interval

A pot of water begins at a temperature ofand is heated at a rate ofdegrees Celsius per minute. What will the temperature of the water be after 4 minutes?

Possible Answers:

有限公司rrect answer:

Explanation:

Letdenote the temperature of the pot afterminutes.

The first thing to realize is that the quantityis the derivative of. Using the fundamental theorem of Calculus, we know that

From there, we just need to solve the integral. Letting u = t+1, du=dt, we have the following:

Where the second equality follows by the power rule, and re-substituting t+1 = u.

Thus, we now have the equation. Because we know that the water started at, all we need to do is rearrange and substitute.

的最后一个swer,

1 3 Next →
Learning Tools by Varsity Tutors