Unformatted text preview: ax + b ) dx = Z 1 a sin u du = 1 a (cos u ) + C =1 a cos( ax + b ) + C. EXAMPLE 8.3 Evaluate Z x sin( x 2 ) dx . Let u = x 2 so du = 2 x dx or x dx = du/ 2. Then Z x sin( x 2 ) dx = Z 1 2 sin u du = 1 2 (cos u ) + C =1 2 cos( x 2 ) + C. EXAMPLE 8.4 Evaluate Z cos( πt ) sin 2 ( πt ) dt . Let u = sin( πt ) so du = π cos( πt ) dt or du/π = cos( πt ) dt . Then Z cos( πt ) sin 2 ( πt ) dt = Z 1 π 1 u 2 du = Z 1 π u2 du = 1 π u11 + C =1 uπ + C =1 π sin( πt ) + C....
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 Spring '07
 JonathanRogawski
 Math, Calculus, Algebra, dx

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