# Advanced Placement Calculus AB Practice

## Section II Part A

1. Let f be the functions given by:

Find the area of the region enclosed by the graphs of f(x) and -f(x).

2. Let f and g be the functions given by:

Let R be the region in the first and second quadrants enclosed by the graphs of f and g. Find the area of R.

3. Let f and g be the functions given by:

Let R be the region in the first and second quadrants enclosed by the graphs of f and g. Find the volume of the solid generated when R is revolved about the x axis.

4. Let f be a function derivabile on the (0, .6) interval. If f '(x) = 3 + ln(x + 1) and f(.1) = 2, what is f(.6)?.

5. Let R be the region in the first quadrant bounded by the y axis and the graphs of f(x) = 3 + ln(x + 1) and g(x) = 2

^{3x}. Find the area of R.

6. Let R be the region in the first quadrant bounded by the y axis and the graphs of f(x) = 3 + ln(x + 1) and g(x) = 2

^{3x}. Region R is the base of a solid. For this solid, each cross-section perpendicular to the x-axis is a square. Find the volume of this solid.

7. A checking account has $120,000 at time t=0. During the interval 0 ≤ t ≤ 18 months, money is deposited into the checking account at a rate d(t) = 2,000(t+1)sin(t/4) dollars/month. At the same time, money is withdrawn from the checking account at the rate w(t) = 10,000/(t+1) dollars/month.

Is the dollar amount increasing at t=9 months? How many dollars are in the account at time t=18 months?

Verify your answers.

The official AP Calculus webpage