school
Acemy

Volumes by Disk and Washer Methods

AP Calculus AB· difficulty 3/5

Region bounded by y=xy = x and y=x2y = x^2 revolved about the xx-axis. Volume?

  • A

    2π15\tfrac{2\pi}{15}

    check_circle
  • B

    π2\tfrac{\pi}{2}

  • C

    π3\tfrac{\pi}{3}

  • D

    π6\tfrac{\pi}{6}

Explanation

Outer y=xy = x, inner y=x2y = x^2 on [0,1][0, 1]. V=π∫01(x2−x4) dx=π(1/3−1/5)=2π/15V = \pi\int_0^1 (x^2 - x^4)\,dx = \pi(1/3 - 1/5) = 2\pi/15.

Want 10 more like this — adaptive to your weak spots?

Practice 10 like thisarrow_forwardPredict my AP score

Related questions

auto_awesomeAll Toolsquestion_answerHomework Q&Amenu_bookAP & SAT PreptimelineLearn Mode