Use the change of variables formula to evaluate the following definite integrals: $\int_{0}^{\frac{\pi}{2}} 2Sin(x)Cos(x)Cos(Sin^2(x))dx$ Sin(1) -Cos(1) -Sin(1) Cos(1)
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Then, $du = 2\sin(x)\cos(x)dx$. When $x = 0$, $u = \sin^2(0) = 0$. When $x = \frac{\pi}{2}$, $u = \sin^2(\frac{\pi}{2}) = 1$. So, the integral becomes $\int_{0}^{1} \cos(u) du$. Show more…
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