math

posted by .

find the volume of the solid by rotating y=1-x^2, y=0 around the xaxis

  • math -

    using discs, of thickness dx

    v = ∫[-1,1] πr^2 dx
    where r = y = 1-x^2
    So,

    v = π∫[-1,1] (1-x^2)^2 dx = 16/15 π

    Using shells, of thickness dy, we have to account for the two branches of the parabola, so it's easier just to use symmetry and get

    v = 2∫[0,1] 2πrh dy
    where r = y and h = x = √(1-y)
    v = 4π∫[0,1] y√(1-y) dy = 16/15 π

  • math -

    pi y^2 dx from -1 to +1
    same as 2 pi y^2 dx from 0 to 1

    2 pi (1-2 x^2 + x^4) dx from 0 to 1

    2 pi (1-0) - 4 pi (1^3/3-0) + 2 pi (1^5/5-0)

    2 pi - 4 pi/3 + 2 pi/5

    (pi/15) ( 30 - 20 + 6)

    (16/15) pi

    Check my arithmetic !

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    This problem set is ridiculously hard. I know how to find the volume of a solid (integrate using the limits of integration), but these questions seem more advanced than usual. Please help and thanks in advance! 1. Find the volume of …
  2. Calculus

    A solid is formed by rotating the region bounded by the curve y=e−3x2 and the x-axis between x=0 and x=1, around the x-axis. The volume of this solid is 3(1−e−3). Assuming the solid has constant density , find x and …
  3. Calculus

    solid is formed by rotating the region bounded by the curve y=e−3x^2 and the x-axis between x=0 and x=1, around the x-axis. The volume of this solid is 3(1−e^−3). Assuming the solid has constant density , find x and …
  4. Calculus

    solid is formed by rotating the region bounded by the curve y=e−3x^2 and the x-axis between x=0 and x=1, around the x-axis. The volume of this solid is 3(1−e^−3). Assuming the solid has constant density , find x and …
  5. 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 …
  6. calculus 2

    Find the volume of the solid formed by rotating the region enclosed by y=e^(5x) , \ y=0, \ x=0, \ x=0.8 around the y-axis Please help, i have been attempting these problems for a couple of days
  7. Calculus [Finding volume of solid]

    Find the volume of the solid formed by rotating the region enclosed by x=0 x=1 y=0 y=4+x^5
  8. 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 …
  9. 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 …
  10. Math

    Let R be the region bounded by y = ln x, x-axis, and x = 3. Answer the following. a) Write, but do not solve, an integral expression that will find the volume of the solid that results from rotating R about x = -2. b) Write, but do …

More Similar Questions