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Fundamental Theorem of Calculus and Accumulation Functions

AP Calculus AB· difficulty 3/5

Let F(x)=∫0xsin⁡(t2) dtF(x) = \int_0^x \sin(t^2)\,dt. Then F′(x)=F'(x) =

  • A

    cos⁡(t2)\cos(t^2)

  • B

    2xcos⁡(x2)2x \cos(x^2)

  • C

    sin⁡(x)\sin(x)

  • D

    sin⁡(x2)\sin(x^2)

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Explanation

FTC1: derivative of integral function = integrand at upper limit.

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