Calculus

posted by James

Write the integral in one variable to find the volume of the solid obtained by rotating the first-quadrant region bounded by y = 0.5x^2 and y = x about the line x = 5.

  1. Steve

    using shells,
    v = ∫[0,2] 2πrh dx
    where r = 5-x and h=x-0.5x^2

    or, using discs,
    v = ∫[0,2] π(R^2-r^2) dy
    where R=5-y and r=5-√(2y)

Respond to this Question

First Name

Your Answer

Similar Questions

  1. calculus

    Sketch the region bounded by the curves y = x^2, y = x^4. 1) Find the area of the region enclosed by the two curves; 2) Find the volume of the solid obtained by rotating the above region about the x-axis; 3) Find the volume of the …
  2. Calculus

    a) Find the volume formed by rotating the region enclosed by x = 6y and y^3 = x with y greater than, equal to 0 about the y-axis. b) Find the volume of the solid obtained by rotating the region bounded by y = 4x^2, x = 1, and y = 0 …
  3. CALCULUS MAJOR HELP!!!!!!

    Find the volume of the solid obtained by rotating the region bounded y = 16 x and y = 2 x^2 about y =0 Find the volume of the solid obtained by rotating the region bounded about the x-axis by y=4x^2, x =1, and y = 0 Find the volume …
  4. Calculus volume stuff

    Find the volume of the solid obtained by rotating the region bounded y = 16 x and y = 2 x^2 about y =0 Find the volume of the solid obtained by rotating the region bounded about the x-axis by y=4x^2, x =1, and y = 0 Find the volume …
  5. Calculus I don't understand

    Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = 10 x and y = 5 x^2 about y =0 Find the volume of the solid obtained by rotating the region bounded by y=8 x^2, x …
  6. Calculus

    Consider the solid obtained by rotating the region bounded by the following curves about the line x=1. y=x,y=0,x=4,x=6 Find the volume So it would be pi (integral from 3 to 6) of ((1-y)^2 -(1-0)^2) right?
  7. calculus review please help!

    1) Find the area of the region bounded by the curves y=arcsin (x/4), y = 0, and x = 4 obtained by integrating with respect to y. Your work must include the definite integral and the antiderivative. 2)Set up, but do not evaluate, the …
  8. calculus review please help!

    Write the integral in one variable to find the volume of the solid obtained by rotating the first‐quadrant region bounded by y = 0.5x2 and y = x about the line x = 5. Use the mid-point rule with n = 4 to approximate the area of the …
  9. Please help Calculus

    Write the integral in one variable to find the volume of the solid obtained by rotating the first‐quadrant region bounded by y = 0.5x2 and y = x about the line x = 5.
  10. Calculus

    Write the integral in one variable to find the volume of the solid obtained by rotating the first-quadrant region bounded by y = 0.5x^2 and y = x about the line x = 7. I have to use the volume by disks method, but I'm confused about …

More Similar Questions