(§5.7, Q98) Show that the two regions in Figure 4 have the same area, i.e., show that V1 – x² dx : cos u du. Then, use the identity cos2 u = (1+ cos 2u) to compute the second area. (HINT: use the substitution x = sin u, for which u(0) = 0 and u(1) = 5.)

Calculus: Early Transcendentals
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Author:James Stewart
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Chapter1: Functions And Models
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(§5.7, Q98) Show that the two regions in Figure 4 have the same area, i.e., show that
2
V1 – x² dx =
cos? u du.
Then, use the identity cos? u = ;(1+ cos 2u) to compute the second area.
(HINT: use the substitution x = sin u, for which u(0) = 0 and u(1) = 5.)
Transcribed Image Text:(§5.7, Q98) Show that the two regions in Figure 4 have the same area, i.e., show that 2 V1 – x² dx = cos? u du. Then, use the identity cos? u = ;(1+ cos 2u) to compute the second area. (HINT: use the substitution x = sin u, for which u(0) = 0 and u(1) = 5.)
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