8.2TrigIntegralsSolutions

8.2TrigIntegralsSolutions - MthSc 108-Learning Activity...

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Unformatted text preview: MthSc 108-Learning Activity Solutions Section 8.2: Trigonometric Integrals 1. Solution: Use the Pythagorean Identity: cos 2 x + sin 2 x = 1 sin 3 xdx = sin 2 x sin xdx = 1- cos 2 x ( ) sin xdx = sin xdx - cos 2 x sin xdx = - du + u 2 du = - u + u 3 3 + C = - cos x + cos 3 x 3 + C where u = cos x and du = - sin xdx . sin 3 xdx = - cos x + cos 3 x 3 + C 2. Solution: Use the Half Angle Formula: cos 2 x = 1 + cos2 x 2 cos 2 xdx = 1 + cos2 x 2 dx = 1 2 dx + 1 2 cos2 xdx = 1 2 x + 1 4 sin 2 x + C cos 2 xdx = 1 2 x + 1 4 sin 2 x + C 3. Solution: Use the Pythagorean Identity: 1 + tan 2 x = sec 2 x tan 4 xdx = tan 2 x tan 2 xdx = tan 2 x sec 2 x- 1 ( ) dx = tan 2 x sec 2 xdx - tan 2 xdx = tan 2 x sec 2 xdx - sec 2 x- 1 ( ) dx = tan 2 x sec 2 xdx - sec 2 xdx + dx = tan 3 x 3- tan x + x + C where u = tan x and du = sec 2 xdx ....
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This note was uploaded on 01/30/2011 for the course MTHSC 108 taught by Professor Any during the Spring '08 term at Clemson.

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8.2TrigIntegralsSolutions - MthSc 108-Learning Activity...

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