Calculus

posted by .

alright. i need to write a definite integral for the volume and evaluate the integral for the region bounded by y=x^2, y=0, and x=1 revolved about the a) x-axis, b) the y-axis, c) x=2, and d) y=-2.
HELP!

Lets do the x=2 axis.

dV= pi rh dr where r is radius, h is height. r= x-1 dr=dx h= y=x^2
dV= PI (x-1)x^2 dx
Then integrate from x=1 to 2

So the idea is to draw the pic, make an incremental dV in terms of r and h, change those to x,y variables.

What about rotating about y=6
dV= PI r h dr
r= 6-y y goes from 0 to 1^2
dr= dy
h= 1-sqrt(y)
check that picture

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. MATH

    Find the volumes of the solids generated by revolving the region in the first quadrant bounded by the following about the given axes. x = y - y3, x = 1, y = 1 (b) Revolved about the y-axis ?
  2. Calculus AP

    Let R be the region in the first quadrant bounded by the graph y=3-√x the horizontal line y=1, and the y-axis as shown in the figure to the right. Please show all work. 1. Find the area of R 2. Write but do not evaluate, an integral …
  3. 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
  4. Calculus check

    The functions f and g are given by f(x)=sqrt(x^3) and g(x)=16-2x. Let R be the region bounded by the x-axis and the graphs of f and g. A. Find the area of R. B. The region R from x=0 to x=4 is rotated about the line x=4. Write, but …
  5. Calculus check and help

    Let R be the region bounded by the curves y=lnx^2 and y=x^2-4 to the right of the y-axis. A. Find the area of R. B. Find the folume geneated when R is rotated about the line y=-4. C. Write, but do not evaluate the integral expression …
  6. calculus

    the region bounded by the graph f(x)=x(2-x) and the x axis is revolved about the y axis. Find the volume of the solid. I did the integral using the shell method, but the answer wasn't correct.
  7. Calculus

    The semicircular region bounded by the curve x=sqrt{9-y^2} and the y-axis is revolved about the line x=-3. The integral that represents its volume is V= ∫ [a^b] f(y) dy What is f(y)?
  8. 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 …
  9. 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. goo.gl/photos/v5qJLDztqsZpHR9d7 …
  10. Calculus

    'Find the volume of the solid generated by revolving the region bounded by x=16-y^2, x-axis, and y-axis around the x-axis.' I know in theory how to do it, but I'm a little confused by what constitutes the bounded region because it's …

More Similar Questions