By William Ma — McGraw-Hill Professional

Updated on Apr 25, 2014

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.

Use a midpoint Riem ann sum with three subdivisions of equal length to find the approximate value of

- 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
- Given
- Let
*f*be a continuous function defined on [0, 30] with selected values as shown below:

**(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.

- Find all values of
- (Calculator) Given the equation 9
*x*^{2}+4*y*^{2}– 18*x*+16*y*=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?
- Evaluate
- Determine the speed of an object moving along the path described by
*x*=3 – 2*t*^{2},

Solutions for these practice problems can be found at: Definite Integrals Solutions to 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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