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Knowing that sin2x+cos2x=1 \sin^2 x + \cos^2 x = 1 sin2x+cos2x=1, then which of the following is true?
(A): ∫0π/2sin2x dx+∫0π/2cos2x dx=π2\displaystyle \int_0^{\pi /2} \sin^2 x \, dx + \int_0^{\pi /2} \cos^2 x \, dx = \dfrac\pi2 ∫0π/2sin2xdx+∫0π/2cos2xdx=2π. (B): ∫0π/2sin2x dx=π4\displaystyle \int_0^{\pi /2} \sin^2 x \, dx = \dfrac\pi4∫0π/2sin2xdx=4π. (C): ∫0π/2cos2x dx=π4\displaystyle \int_0^{\pi /2} \cos^2 x \, dx = \dfrac\pi4∫0π/2cos2xdx=4π.
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