# Calculus

The region enclosed by the graph of y = x^2 , the line x = 2, and the x-axis is revolved abut the y-axis. The volume of the solid generated is:

A. 8pi
B. 32pi/5
C. 16pi/3
D. 4pi
5. 8pi/3

I solved for x as √y and set up this integral:

2pi * integral from 0 to 2 of y√y.

But it doesn't seem to give the answer, and I'm not sure what's wrong with it.

1. 👍 0
2. 👎 0
3. 👁 1,201
1. Using shells of thickness dx,

v = ∫[0,2] 2πrh dx
where r=x and h=y=x^2
v = ∫[0,2] 2πx^3 dx = 8π

using discs (washers) of thickness dy,

v = ∫[0,4] π(R^2-r^2) dy
where R=2 and r=x=√y
v = ∫[0,4] π(4-y) dy = 8π

You appear to have tried to rotate around the x-axis.

1. 👍 0
2. 👎 0
2. also, if you did that rotation, the height of the shells would be 2-x, not x.

1. 👍 0
2. 👎 0

## Similar Questions

1. ### Calculus

Find the area of the indicated region. We suggest you graph the curves to check whether one is above the other or whether they cross, and that you use technology to check your answer. Enclosed by y = x^2 − 4x + 1 and y = −x^2

2. ### calculus

find the value of m so that the line y = mx divides the region enclosed by y = 2x-x^2 and the x-axis into two regions with equal area i know that the area enclosed by y=2x-x^2 is 4/3 so half of that would be 2/3 however, i have no

3. ### pre-calc

area of a rectangular region: a farmer wishes to create two rectangular regions bordering a river, by three fences perpendicular to the river and one connecting them. suppose that x represents the length of each of the three

4. ### Calculus

Sketch the region enclosed by the curves x= 49-y^2 and x = y^2 - 49. Decide whether to integrate with respect to x or y. Then find the area of the region.

1. ### math

Find the area of the region enclosed between y=2sin(x) and y=3cos(x) from x=0 to x=0.7π. Hint: Notice that this region consists of two parts.

2. ### Calculus

The base of a solid is the region enclosed by the graph of x^2 + 4y^2 = 4 and cross-sections perpendicular to the x-axis are squares. Find the volume of this solid. a. 8/3 b. 8 pi/3 c. 16/3 d. 32/3 e. 32 pi/3 Thanks in advance! :)

3. ### calculus

R is the first quadrant region enclosed by the x-axis, the curve y = 2x + a, and the line x = a, where a > 0. Find the value of a so that the area of the region R is 18 square units.

4. ### calc

1. Let R be the region bounded by the x-axis, the graph of y=sqr(x) , and the line x=4 . a. Find the area of the region R. b. Find the value of h such that the vertical line x = h divides the region R into two regions of equal

1. ### calculus

Let R be the region in the first quadrant that is enclosed by the graph of y = tanx, the x-axis, and the line x = π/3 h. Find the area of R i. Find the volume of the solid formed by revolving R about the x-axis

2. ### calculus

let R be the region bounded by the x-axis, the graph of y=sqrt(x+1), and the line x=3. Find the area of the region R

3. ### Calc AB

What is the area of the region in the first quadrant enclosed by the graph of y=e^(x^2/4) and the line y=0.5? When I graphed the two functions they don't even connect so the answer would be infinity. What am I doing wrong>

4. ### Math

Find the volume of the solid obtained by rotating the region enclosed by y=x^2, y=6x about the line x=0using the method of disks or washers.