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The goal of this problem is to evaluate 1 Because the sine term has an...

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Calculus

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The goal of this problem is to evaluate 1 Because the sine term has an odd power the first step is to rewrite sin x sin x sin x sin x sin x where n 3 2 Next replace the sin x term with 1 cos x 3 Now do a substitution with u sin a cos a da using substitution u cos x and du sin x dx 4 With this substitution the integral after multiplying out into a sum of powers of u becom SE u Do not put a negative sign in front of the integral 5 Now antidifferentiate in terms of u and substitute back to get the final result sin x cos x dx C

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