school
Acemy

Volumes with Cross Sections

AP Calculus AB· difficulty 3/5

Solid has base bounded by y=1−x2y = 1 - x^2 and y=0y = 0. Cross-sections perpendicular to xx-axis are squares (side = base width). Volume?

  • A

    23\tfrac{2}{3}

  • B

    1615\tfrac{16}{15}

    check_circle
  • C

    815\tfrac{8}{15}

  • D

    43\tfrac{4}{3}

Explanation

Side =1−x2= 1 - x^2. V=∫−11(1−x2)2 dx=2∫01(1−2x2+x4) dx=2(1−2/3+1/5)=2(8/15)=16/15V = \int_{-1}^{1}(1-x^2)^2\,dx = 2\int_0^1 (1 - 2x^2 + x^4)\,dx = 2(1 - 2/3 + 1/5) = 2(8/15) = 16/15.

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