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Mathematics

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Trigonometric Substitution Suppose √x=siny. (a) Use the substitution x=sin2 y,dx=2 sin y cos ydy to show ∫1/2 0 √xdx/√1−x = ∫π/4 0 2 sin2 ydy (b) Use the identity given in Exercise 49 to evaluate the definite integral without a calculator.

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