Calculus

posted by .

*Note I reposted this question as I changed the subject**


The Region "R" under the graph of y = x^3 from x=0 to x=2 is rotated about the y-axis to form a solid.

a. Find the area of R.
b. Find the volume of the solid using vertical slices.
c. Find the first moment of area of R with respect to the y-axis. What do you notice about the integral?
d. Find the x coordinate of the centroid of R.
e. A theorem of Pappus states that the volume of a solid of revolution equals the area of the region being rotated times the distance the centroid of the region travels. Show that this problem confirms this theorem.

I was able to do part "a" as the integral from 0 to 2 of x^3 dx. Also I believe part "b" is pi*[3y^(5/3)/5] evaluated from 0 to 2

  • Calculus -

    Help.

  • Calculus -

    Too advanced for you?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. please help calculus

    find the volume of the solid formed by revolving the region bounded by y=e^x, y=0, x=o and x=1 about the y axis by using the shell method, i got v=2*pi int(o to 1) (x)(e^x) dx and my teacher said the answer is e/2 but i keep getting …
  2. 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 …
  3. First Moment

    The Region "R" under the graph of y = x^3 from x=0 to x=2 is rotated about the y-axis to form a solid. a. Find the area of R. b. Find the volume of the solid using vertical slices. c. Find the first moment of area of R with respect …
  4. calculus

    Find the volume of the solid obtained by rotating the region under the graph f(x) = x2 - 3x about the x-axis over the interval [0, 3].
  5. Calculus

    Let R be the region bounded by the x-axis, x = 5 and the curve y = x. This region is rotated around the x-axis. Find the volume of the resulting solid. (Note: R is a triangular region. The resulting solid has a simple shape. You may …
  6. Calculus Help!!

    Region R is bounded by the functions f(x) = 2(x-4) + pi, g(x) = cos^-1(x/2 - 3), and the x axis. a. What is the area of the region R?
  7. Calculus

    Find the volume of the solid obtained by rotating the region under the graph of the function f(x) = (2)/(x+1) about the x-axis over the interval [0,3]
  8. Math

    Find the volume of the solid generated by revolving the region bounded by y=x+(x/4), the x-axis, and the lines x=1 and x=3 about the y-axis. I've drawn the graph and I understand which part is being rotated, but I'm having trouble …
  9. Calculus

    Find the volume of the solid obtained by rotating the region under the graph of f(x)= 9-x^2 for 0<= x<=3 about the vertical axis x= -2. My answer: 81 pi/2
  10. calculus

    The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method. y = −x2 + 7x − 12, y = 0; about the x-axis

More Similar Questions