Calculus

Can you check if I set up the integral correctly? Thanks!

He carved a parabola out of the cover of his teacher’s edition. It spins around the antenna in the wind. Find the volume of this solid of revolution if the equation of the parabola is x=1-y^2 and the antenna is the y-axis.

2Pi integral (0 to 1) (1-x^2)^2 dy =16pi/15

  1. 👍 0
  2. 👎 0
  3. 👁 197
  1. x=0 at y = -1 and +1
    The base of the parabola is at x =0 and it extends to a vertex at (x=1, y=0)

    As you rotate about x=0, you generate cylindrical shell elements of the solid of revolution with volume

    dV = (2 pi x) * 2 sqrt (1-x)dx
    V = (Integral of) 4 pi x*sqrt(1-x) dx
    0 to 1
    substitute 1-x = u
    = (Integral of) 4 pi (u-1) *sqrt u du
    1 to 0
    = (4/15)(4 pi) = 16 pi/15

    I agree with your answer but see that you integrated slabs running in the y direction. That would work, but it seems to me that your (1-x^2)^2 in the integral should be (1-y^2)^2

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Ed Tech plz helppppp

    What does it mean to troubleshoot your computer? identify problems with your computer and attempt to fix them*** to open your computer to see what's missing from the hard drive to switch the mouse and keyboard plugs to download

  2. Calculus

    Find expressions for the quadratic functions whose graphs are shown. One graph has the point (4,2) plotted in which the parabola passes through (U-shaped parabola- right side up) The vertex is at (3,0) and the parabola does not

  3. Physics, Calculus(alot of stuff together)= HELP!!

    A rod extending between x=0 and x= 14.0cm has a uniform cross- sectional area A= 9.00cm^2. It is made from a continuously changing alloy of metals so that along it's length it's density changes steadily from 2.70g/cm^3 to

  4. English

    Identify the sentence that is correctly punctuated. A. It is not always necessary; however, to check the entire set of books. B. It is not always necessary, however; to check the entire set of books. C. It is not always necessary,

  1. calc: avg value

    Find the average value of the function "f(x) = x^2 sqrt(1+x^3)" on the interval [0,2]. and this is what i did.. please check for mistakes. thanks :D f(x) = x^2 sqrt(1+x^3), [0,2] f ave = (1/(b-a))*inegral of a to b for: f(x) dx f

  2. Calculus

    If f(x) and g(x) are continuous on [a, b], which one of the following statements is true? ~the integral from a to b of the difference of f of x and g of x, dx equals the integral from a to b of f of x, dx minus the integral from a

  3. Math (Calculus II) (Volume Revolution Setup)

    Consider the graph of y^2 = x(4-x)^2 (see link). Find the volumes of the solids that are generated when the loop of this graph is revolved about (a) the x-axis, (b) the y-axis, and (c) the line x = 4.

  4. Calculus

    Given the equation xy = 2, set up an integral to find the length of path from x = a to x = b and enter the integrand below. I did the integral from b to a and set it equal to the sqrt(1+4/x^4), because I found y to equal 2/x and

  1. calc: arc length

    find the exact length of this curve: y = ( x^3/6 ) + ( 1/2x ) 1/2

  2. Math

    14) Consider the parabola with equation y = x^2 - 6x + 5. a. Use any suitable method to determine the coordinates of the turning point of this parabola. b. Hence, state for which values of c the line y = c will intersect the

  3. Calculus II

    Hi, not sure how to set this integral up for my Calculus II homework. "Given a graph that contains a parabola and a line, the equation of the parabola is x=(y-3)²/4 and the equation of the line is y=6-x. Find the area of the

  4. calculus

    using the method of shells, set up, but don't evaluate the integral, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. Y=e^x, x=0, y=2, about y=1

You can view more similar questions or ask a new question.