Definite Integrals Practice Problems for AP Calculus
Review the following concepts if needed:
- Riemann Sums and Definite Integrals for AP Calculus
- Fundamental Theorem of Calculus for AP Calculus
- Evaluating Definite Integrals for AP Calculus
- Improper Intervals: Infinite Intervals of Integration and Infinite Discontinuities for AP Calculus
Part A The use of a calculator is not allowed.
Evaluate the following definite integrals.
- If f' (x )=g (x ) and g is a continuous function for all real values of x , express
- Use a midpoint Riemann sum with four subdivisions of equal length to find the approximate value of
- Let f be a continuous function defined on [0, 30] with selected values as shown below:
Use a midpoint Riem ann sum with three subdivisions of equal length to find the approximate value of
(Calculator) indicates that calculators are permitted.
- The graph of f' , the derivative of f' , 6 ≤ x ≤ 8 is shown in Figure 11.7-1.
- Find all values of x such that f attains a relative maximum or a relative minimum.
- Find all values of x such that f is concave upward.
- Find all values of x such that f has a change of concavity.
- (Calculator) Given the equation 9x2 +4y2 – 18x +16y =11, find the points on the graph where the equation has a vertical or horizontal tangent.
- (Calculator) Two corridors, one 6 feet wide and another 10 feet wide meet at a corner. See Figure 11.7-2. What is the maximum length of a pipe of negligible thickness that can be carried horizontally around the corner?
- Determine the speed of an object moving along the path described by x =3 – 2t2,
Solutions for these practice problems can be found at: Definite Integrals Solutions to Practice Problems for AP Calculus