All AP Calculus AB Resources
Example Questions
Example Question #12 : Interpretations And Properties Of Definite Integrals
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Example Question #13 : Interpretations And Properties Of Definite Integrals
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Example Question #14 : Interpretations And Properties Of Definite Integrals
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Example Question #15 : Interpretations And Properties Of Definite Integrals
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Example Question #16 : Interpretations And Properties Of Definite Integrals
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Example Question #17 : Interpretations And Properties Of Definite Integrals
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Example Question #21 : Interpretations And Properties Of Definite Integrals
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Example Question #21 : Interpretations And Properties Of Definite Integrals
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Example Question #23 : Interpretations And Properties Of Definite Integrals
A pot of water begins at a temperature of
and is heated at a rate of degrees Celsius per minute. What will the temperature of the water be after 4 minutes?
Possible Answers:
Correct answer:
Explanation:
Let
denote the temperature of the pot after minutes.
The first thing to realize is that the quantity
is 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.
Yielding our final answer,
Example Question #61 : Integrals
A ball is thrown into the air. It's height, after t seconds is modeled by the formula:
h(t)=-15t^2+30t feet.
At what time will the velocity equal zero?
Possible Answers:
1.5s
3s
1s
0s
5s
Correct answer:
1s
Explanation:
In order to find where the velocity is equal to zero, take the derivative of the function and set it equal to zero.
h(t) = –15t2 + 30t
h'(t) = –30t + 30
0 = –30t + 30
Then solve for "t".
–30 = –30t
t = 1
The velocity will be 0 at 1 second.
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