![]() ![]() And then you put theīounds of integration. Then you say what variable is the variable that you're integrating with respect to. And the way that you do it is you first define the function, then you put a comma. So this function, fn integral, this is a integral of a function, or a function integral right over here, so we press Enter. We wanna do definite integrals so I can click math right over here, move down. And lucky for us we can use calculators in this section of the AP exam, so let's bring out a graphing calculator where we can evaluate definite integrals. And so this is going to be equal to the integral from 0 to 8 of 20sin of t squared over 35 dt. That's the power of the definite integral. This is how much flows, what volume flows in overĪ very small interval, dt, and then we're gonna sum it up from t equals 0 to t equals 8. Once again, what am I doing? R of t times D of t, So this expression right over here, this is going to give us how many cubic feet of ![]() And so what we wanna do is we wanna sum up these amounts over very small changes in time to go from time is equal to 0, all the way to time is equal to 8. Small change in time, so Dt, this is the amount that flows in over that very small change in time. If you multiply times some change in time, even an infinitesimally Things are flowing into it, they give it in cubic feet per hour. So if you have your rate, this is the rate at which ![]() So they're asking how manyĬubic feet of water flow into, so enter into the pipe, during But these are the rates ofĮntry and the rates of exiting. There is 30 cubic feet of water right in the beginning. So if that is the pipe right over there, things are flowing in at a rate of R of t, and things are flowing Let me draw a little rainwater pipe here just so that we can How many cubic feet of rainwater flow into the pipe during the 8 hour time interval 0 is less than or equal to t is less than or equal to 8? Alright, so we know the rate, the rate that things flow For the same interval right over here, there are 30 cubic feet It's equal to -0.04t to the third power plus 0.4t squared plusĠ.96t cubic feet per hour. The pipe is partially blocked, allowing water to drain out the other end of the pipe at rate modeled by D of t. Is less than or equal to t, which is less than or equal to 8, so t is gonna go between 0 and 8. To 20sin of t squared over 35 cubic feet per hour. Then compare your solutions with our solutions and notes.- The rate at which rainwater flows into a drainpipe is modeled by the function R, where R of t is equal The best way to practice with the past exam questions is to first solve them on your own, The free-response questions and scoring guidelines for these examsĪre posted on the College Board's apstudent web site and, for teachers, on AP Central: This chapter contains solutions and notes for the free-response questions from past AP Calculus exams. However, you may print out one copy of this chapter for personal use and for face-to-face teaching for each copy of the Be Prepared book that you own or receive from your school. You are not authorized to publish or distribute it in any form without our permission. This material is provided to you as a supplement to the book Be Prepared for the AP Calculus Exam. AP Calculus - Past Free-Response Questions ![]()
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