AP Calculus BC Knowledge Review: Areas, Volumes, and Arc Lengths

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In this chapter, you will be introduced to several important applications of the definite integral. You will learn how to find the length of a curve, the area under a curve, and the volume of a solid. Some of the techniques that you will be shown include finding the area under a curve by using rectangular and trapezoidal approximations, and finding the volume of a solid using cross sections, discs, and washers. These techniques involve working with algebraic expressions and lengthy computations. It is important that you work carefully through the practice problems provided in the chapter and check your solutions with the given explanations.

Key Ideas

The function F(x) = ∫axf(t)dt

Rectangular Approximations

Trapezoidal Approximations

Area Under a Curve

Area Between Two Curves

Solids with Known Cross Sections

The Disc Method

The Washer Method

Area and Arc Length for Parametric and Polar Curves

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