Fundamental Theorem of Calculus and Accumulation Functions

AP Calculus AB· difficulty 3/5

For g(x)=2exlntdtg(x) = \int_2^{e^x} \ln t\,dt, g(x)=g'(x) =

  • A

    ln(ex)\ln(e^x)

  • B

    exln(ex)=xexe^x \ln(e^x) = x e^x

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  • C

    xexx e^x

  • D

    xexx \cdot e^x

Explanation

Chain rule: ln(ex)ex=xex\ln(e^x) \cdot e^x = x e^x.

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