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Integration Practice Problems for AP Calculus

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By — McGraw-Hill Professional
Updated on Oct 24, 2011

Review the following concepts if needed:

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

  1. (x5 + 3x2x + 1)dx
  2. x3 (x4 – 10)5dx
  3. x csc2(x2)dx
  4. (e2x )(e4x)dx
  5. ln(e5x + 1)dx
  6. If = ex + 2 and the point (0, 6) is on the graph of y, find y.
  7. –3ex sin(ex )dx
  8. If f (x) is the antiderivative of and f (1) = 5, find f (e).
  9. 3x2 sin x dx

 

(Calculator) indicates that calculators are permitted.

  1. The graph of the velocity function of a moving particle for 0 ≤ t ≤ 10 is shown in Figure 10.6-1.
  2. Cumulative Review Problems

    1. At what value of t is the speed of the particle the greatest?
    2. At what time is the particle moving to the right?
  3. 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?
  4. Evaluate
  5. (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.
  6. Which of the following is the best approximation for f '(1)?

    1. f '(1) < 2
    2. 0.5 < f '(1) < 1
    3. 1.5 < f '(1) < 2.5
    4. 2.5 < f '(1) < 3.5
    5. f '(1) > 2
  7. 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 ':
  8. Cumulative Review Problems

    1. have a point of inflection?
    2. have a relative maximum or minimum?
    3. concave upward?
  9. Evaluate
  10. If the position of an object is given by x = 4 sin(πt), y = t2 – 3t + 1, find the position of the object at t =2.
  11. 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

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