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Applications of Definite Integrals Practice Problems for AP Calculus (page 2)

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

 

(Calculator) indicates that calculators are permitted.

  1. If 3e y =x 2 y, find .
  2. Evaluate .
  3. The graph of a continuous function f which consists of three line segments on [–2, 4] is shown in Figure 13.10-1. If ,
  4. Cumulative Review Problems

    1. Find F (–2) and F (0).
    2. Find F' (0) and F' (2).
    3. Find the value of x such that F has a maximum on [–2, 4].
    4. On which interval is the graph of F concave upward?
  5. (Calculator) The slope of a function y = f (x) at any point (x, y) is and f(0)=2.
    1. Write an equation of the line tangent to the graph of f at x =0.
    2. Use the tangent in part (a) to find the approximate value of f(0.1).
    3. Find a solution y = f(x) for the differential equation.
    4. Using the result in part (c), find f (0.1).
  6. (Calculator) Let R be the region in the first quadrant bounded by f(x) = e x – 1 and g(x)=3 sin x.
    1. Find the area of region R.
    2. Find the volume of the solid obtained by revolving R about the x -axis.
    3. Find the volume of the solid having R as its base and semicircular cross sections perpendicular to the x -axis.
  7. An object traveling on a path defined by {x(θ), y(θ)} has an acceleration vector of {sin θ, –cos θ}. If the velocity of the object at time is {–1, 0} and the initial position of the object is the origin, find the position when θ = π.
  8. A projectile follows a path defined by x = t – 2, y = sin2 t on the interval 0 ≤ t ≤ π. Find the point at which the object reaches its maximum y -value.

Solutions for these practice problems can be found at:  Solutions to Applications of Definite Integrals Practice Problems for AP Calculus

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