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Integration by Substitution

AP Calculus AB· difficulty 3/5

∫0π/2sin⁡2xcos⁡x dx=\displaystyle\int_0^{\pi/2} \sin^2 x \cos x\,dx =

  • A

    13\tfrac{1}{3}

    check_circle
  • B

    12\tfrac{1}{2}

  • C

    11

  • D

    π/3\pi/3

Explanation

u=sin⁡xu = \sin x, u(0)=0,u(π/2)=1u(0) = 0, u(\pi/2) = 1. ∫01u2 du=1/3\int_0^1 u^2\,du = 1/3.

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