Test your knowledge of surface area and volume of revolutions in calculus with t...
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Questions and Answers

When finding the surface area of revolution, what does the term √(1 + (f'(x))^2) represent?

  • The element of surface area
  • The circumference of the curve
  • The radius of revolution
  • The element of arc length (correct)

    • What is the formula for finding the surface area of revolution when rotating the curve y = f(x) about the x-axis?

  • π∫[a,b] (f(x))^2 (1 + (f'(x))^2) dx
  • 2π∫[a,b] f(x) √(1 + (f'(x))^2) dx (correct)
  • π∫[a,b] (f(x))^2 √(1 + (f'(x))^2) dx
  • 2π∫[a,b] f(x) (1 + (f'(x))^2) dx

    • What is the formula for finding the volume of revolution when rotating the curve y = f(x) about the x-axis?

  • π∫[a,b] (f(x))^3 dx
  • π∫[a,b] f(x) √(1 + (f'(x))^2) dx
  • π∫[a,b] (f(x))^2 dx (correct)
  • π∫[a,b] f(x) dx

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