Integrating Squares

Calculus Level 2

Knowing that sin2x+cos2x=1 \sin^2 x + \cos^2 x = 1 , then which of the following is true?

(A): 0π/2sin2xdx+0π/2cos2xdx=π2\displaystyle \int_0^{\pi /2} \sin^2 x \, dx + \int_0^{\pi /2} \cos^2 x \, dx = \dfrac\pi2 .
(B): 0π/2sin2xdx=π4\displaystyle \int_0^{\pi /2} \sin^2 x \, dx = \dfrac\pi4.
(C): 0π/2cos2xdx=π4\displaystyle \int_0^{\pi /2} \cos^2 x \, dx = \dfrac\pi4.

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