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4int(0)^(a^(2))sin^(2)xdx+int(0)^(2a^(2)...

4int_(0)^(a^(2))sin^(2)xdx+int_(0)^(2a^(2))cos xdx

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Show that int_(0)^((pi)/(2))sin^(2)xdx=int_(0)^((pi)/(2))cos^(2)xdx=pi/4 .

Prove that int_(0)^((pi)/(2))sin^(2)xdx=int_(0)^((pi)/(2))cos^(2)xdx=(pi)/(4)