7.7.77-eg - Example Evaluate √ ds 4 − 9s 2 . We first...

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Unformatted text preview: Example Evaluate √ ds 4 − 9s 2 . We first notice that the integrand resembles d sin−1 u(s) = ds u (s) 1 − u(s)2 . In an effort to convert the expression under radical into the form 1 − u(s)2 , we factor to obtain √ Now let u = ds = 4 − 9s2 ds 4(1 − 9s2 ) 4 = 1 2 ds 1− 3s 2 2 . 3s 3 , then du = ds. A substitution yields 2 2 √ ds 12 =· 2 23 4 − 9s √ 1 1 du 3s = sin−1 u + C = sin−1 +C 2 3 3 2 1−u ...
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