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The goals of the AP Calculus program include the statement, “Students should understand the definite integral … as the net accumulation of change….”[1] The Topical Outline includes the topic the “definite integral of the rate of change of a quantity over an interval interpreted as the [net] change of the quantity over the interval:

”

AP Example from 2008 AB 7

- A particle moves along the x-axis with velocity given by
- for time . If the particle is at the position
- x = 2 at time t = 0, what is the position of the particle
- at time t = 1?

AP Example from 2008 AB 87

An object traveling in a straight line has position

x(t) at time t. If the initial position is x(0) = 2 and

the velocity of the object is , what is

the position of the object at t = 3?

AP Example from 2008 AB 81

- If G(x) is an antiderivative for f (x) and G(2) = -7,
- then G(4) =
- (A) f ´(4) (B) -7 + f ´(4) (C)
- (D) (E)

A quick look at some free-response questions

- 2000 AB 4
- 2008 AB2 / BC2 (d)
- 2008 AB 3 (c)
- 2008 AB4 / BC 4 (a)

A quick look at some free-response questions

- AB 1 (a, c, d)
- AB 2 (c)
- 2010 AB 3 (a,d)
- 2010 AB 5 (a)

and since f ´(x) ≥ 0 on [-4, M ] it follows that f (M) > f (-4).

M

and since on [M, 4] £ 0 it follows that f (M) > f (4)

M

Since M is the only critical number in the interval [-4, 4] and f (M) > f (-4) and f (M) > f (4), x = M is the location of the absolute maximum value by the Candidates’ Test.

M

Lin McMullin

E-mail: [email protected]

Blog: TeachingCalculus.wordpress.com

Website: www.LinMcMullin.net

Click on AP Calculus

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