By William Ma — McGraw-Hill Professional

Updated on Aug 29, 2014

Review the following concepts if needed:

- Evaluating Basic Integrals for AP Calculus
- Integration by U-Substitution for AP Calculus
- Techniques of Integration for AP Calculus

Evaluate the following integrals in problems 1 to 20. No calculators are allowed. (However, you may use calculators to check your results.)

- (
*x*^{5}+ 3*x*^{2}–*x*+ 1)*dx* -
*x*^{3}(*x*^{4}– 10)^{5}*dx* -
*x*csc^{2}(*x*^{2})*dx* - (
*e*^{2x})(*e*^{4x})*dx* - ln(
*e*^{5x + 1})*dx* - If =
*e*+ 2 and the point (0, 6) is on the graph of^{x}*y*, find*y*. - –3
*e*sin(^{x}*e*)^{x}*dx* - If
*f*(*x*) is the antiderivative of and*f*(1) = 5, find*f*(*e*). - 3
*x*^{2}sin*x**dx*

(Calculator) indicates that calculators are permitted.

Which of the following is the best approximation for *f '*(1)?

- The graph of the velocity function of a moving particle for 0 ≤
*t*≤ 10 is shown in Figure 10.6-1.- At what value of
*t*is the speed of the particle the greatest? - At what time is the particle moving to the right?

- At what value of
- Air is pumped into a spherical balloon, whose maximum radius is 10 meters. For what value of
*r*is the rate of increase of the volume a hundred times that of the radius? - Evaluate
- (Calculator) The function
*f*is continuous and differentiable on (0, 2) with*f ''*(*x*) > 0 for all*x*in the interval (0, 2). Some of the points on the graph are shown below.*f '*(1) < 2- 0.5 <
*f '*(1) < 1 - 1.5 <
*f '*(1) < 2.5 - 2.5 <
*f '*(1) < 3.5 *f '*(1) > 2

- The graph of the function
*f ''*on the interval [1, 8] is shown in Figure 10.6-2. At what value(s) of*t*on the open interval (1, 8), if any, does the graph of the function*f '*:- have a point of inflection?
- have a relative maximum or minimum?
- concave upward?

- Evaluate
- If the position of an object is given by
*x*= 4 sin(*πt*),*y*=*t*^{2}– 3*t*+ 1, find the position of the object at*t*=2. - Find the slope of the tangent line to the curve
*r*= 3 cos θ when θ = .

Solutions for these practice problems can be found at: Solutions to Integration Practice Problems for AP Calculus

From 5 Steps to a 5 AP Calculus AB and BC. Copyright © 2010 by The McGraw-Hill Companies. All Rights Reserved.

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