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FTC and Definite Integrals

AP Calculus AB· difficulty 4/5

∫−12∣x∣ dx=\displaystyle \int_{-1}^{2} |x|\, dx =

  • A

    33

  • B

    22

  • C

    32\frac{3}{2}

  • D

    52\frac{5}{2}

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Explanation

Split at 0: ∫−10(−x) dx+∫02x dx=1/2+2=5/2\int_{-1}^0(-x)\,dx + \int_0^2 x\,dx = 1/2 + 2 = 5/2.

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