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# Definite Integrals Practice Problems for AP Calculus

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Review the following concepts if needed:

Part A The use of a calculator is not allowed.

Evaluate the following definite integrals.

1. If f' (x )=g (x ) and g is a continuous function for all real values of x , express
2. Use a midpoint Riemann sum with four subdivisions of equal length to find the approximate value of
3. Given
4. Let f be a continuous function defined on [0, 30] with selected values as shown below:
5. Use a midpoint Riem ann sum with three subdivisions of equal length to find the approximate value of

(Calculator) indicates that calculators are permitted.

1. The graph of f' , the derivative of f' , 6 ≤ x ≤ 8 is shown in Figure 11.7-1.
1. Find all values of x such that f attains a relative maximum or a relative minimum.
2. Find all values of x such that f is concave upward.
3. Find all values of x such that f has a change of concavity.
2. (Calculator) Given the equation 9x2 +4y2 – 18x +16y =11, find the points on the graph where the equation has a vertical or horizontal tangent.
3. (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?
4. Evaluate
5. 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

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