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Volumes with Cross Sections

AP Calculus AB· difficulty 3/5

A solid has base in the xyxy-plane bounded by y=f(x)y = f(x) and the xx-axis on [a,b][a, b]. Cross-sections perpendicular to the xx-axis are <strong>squares</strong> with side f(x)f(x). Volume is

  • A

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

    check_circle
  • B

    ∫abπ[f(x)]2 dx\int_a^b \pi [f(x)]^2\,dx

  • C

    ∫ab2f(x) dx\int_a^b 2 f(x)\,dx

  • D

    ∫abf(x) dx\int_a^b f(x)\,dx

Explanation

Square cross-section area =s2=[f(x)]2= s^2 = [f(x)]^2. Integrate.

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