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# 2011 Calculus AB Free Response #1 (b, c, & d)

Integration to find average value of a function. Using a graphing calculator to calculate definite integrals. Created by Sal Khan.

## Want to join the conversation?

• at shouldn't it be 6pi/6 + pi/6? ... just my small ocd
• Yes
• In part d, Sal takes the definite integral of V(t) to get the position function but includes a constant c which he solves for later. When a constant of integration isn't required for definite integrals why does Sal include one? Or is this something I don't know..?
• Let me try to explain it another way. When you're integrating a velocity function from [A,B], think of it as finding the distance traveled when the particle was in between A and B, and not counting the distance that the particle already STARTED at. The constant was added because the integrating part finds out where the patricle traveled to and how far, while the constant adds in the place where the particle started to move from.
(1 vote)
• I don't understand how the equation is set up in part d. Could someone explain?
• The integral of v(t) tells us the displacement or position of the particle. The anti-derivative is missing the constant because we don't know the constant for the initial function. However, when given the initial constant x(0)=2, we know the beginning position along the horizontal position. This should hopefully explain why the equation is set up that way.
(1 vote)
• b: correct me if im wrong .
for t beetween 0 to 6 the particle has some negative movement(x<0)
I think if we differ beetwen speed and velocity in part "A" we must keep the same criteria in part B.
they request the avrage velocity and not avrage Speed.So :just find the distance beetween t=0 and t=6 and devide it to 6.and forget about the displacement of particle going and coming back,just the difference beetween start taime and end Time.
AM I CORRECT?
• Would this have been a question where a calculator is permitted?
(1 vote)
• yeah, it even says you need a graphing calculator
• how did he calculated fast 7(pi)/6? :D
(1 vote)
• When he did pi + pi/6, he changed the common denominator, but failed to indicate that when he wrote 6pi + pi/6. It should be 6pi/6 + pi/6, which is how he ended up with 7pi/6.
• Just a question, 1a's answer is speed is increasing from previous video right? Then why does he have the answer on a as "decreasing" in this video? It's kind of confusing.