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Volumes with Cross Sections

AP Calculus AB· difficulty 4/5

x side s(x)

A solid has square cross-sections perpendicular to the xx-axis with side s(x)s(x). Volume equals:

  • A

    π∫abs(x)2 dx\pi \int_a^b s(x)^2\,dx

  • B

    ∫abs(x) dx\int_a^b s(x)\,dx

  • C

    ∫ab[s(x)]2 dx\int_a^b [s(x)]^2\,dx

    check_circle
  • D

    ∫ab4s(x) dx\int_a^b 4s(x)\,dx

Explanation

Square cross-sections: A(x)=s(x)2A(x) = s(x)^2, so V=∫abs(x)2 dxV = \int_a^b s(x)^2\,dx.

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