Barrons AP Calculus
Figure N7–9 Example 5 __ A solid has as its base the circle x^2 + y^2 = 9, and all cross sections parallel ...
. Questions 25, 26, and 27 in the Practice Exercises illustrate solids with known cross sections. When the cr ...
Example 6 __ Find the volume of a sphere of radius r. SOLUTION: If the region bounded by a semicircle (with ...
Figure N7–13 SOLUTION: Disk. See Questions 18, 49, 51, 52, and 53 in the Practice Exercises for examples of finding ...
Figure N7–14 This washer’s height is the thickness of the rectangular strip, Δx. The washer is a disk whose ...
Figure N7–15 Example 9 __ Find the volume of the solid generated when the region bounded by y = x^2 , x ...
Figure N7–16 See Questions 19, 21, 48, 50, and 54 in the Practice Exercises for examples in which washers are reg ...
Figure N7–17 This shell’s radius, r, is the distance from the axis to the rectangular strip, and its height is ...
Example 11 __ The region bounded by y = 3x − x^2 and y = x is rotated about the y-axis. Find the volum ...
Figure N7–20 (Note that we obtained the same result using washers in Example 8.) NOTE: In Examples 32 a ...
Here a small piece of the curve is equal approximately to . As Δx → 0, the sum of these pieces approa ...
Example 14 __ Find the length, to three decimal places, of the curve (x − 2)^2 = 4y^3 from y = 0 t ...
D. IMPROPER INTEGRALS Improper integral There are two classes of improper integrals: (1) those in which a ...
Note, however, that each integral of the following set is proper: The integrand, in every exa ...
Figure N7–22 BC ONLY Example 18 __ . Then diverges. It can be proved that converges if p > 1 but ...
Figure N7–23 Example 19 __ . Example 20 __ . BC ONLY ...
Example 21 __ Example 22 __ . Thus, this improper integral diverges. Example 23 __ . Since this limit doe ...
BC ONLY Example 24 __ Find . SOLUTION:. In Figure N7–24 we interpret this integral as the first-quadrant ...
Does converge or diverge? SOLUTION:. Therefore, this integral diverges. It can be shown that conver ...
Example 26 __ . Example 27 __ . This integral diverges. Example 28 __ Example 29 __ . Neither limit exists; the inte ...
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