Calculus
posted by Jillian .
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 the solid formed by rotating around the xaxis the region enclosed by the graphs of y = 1 + SQRT(x), the xaxis, the yaxis, and the line x = 4.
a. 7.667
b. 9.333
c. 22.667
d. 37.699
e. 71.209
2. Find the volume of the solid formed by rotating around the yaxis the region bounded by y = 1 + SQRT(x), the yaxis, and the line y = 3.
a. 6.40
b. 8.378
c. 20.106
d. 100.531
e. 145.77
3. Find the volume of the solid formed by rotating around the line y = 5 the region bounded by y = 1 = SQRT(x), the yaxis, and the line y = 3.
a. 13.333
b. 17.657
c. 41.888
d. 92.153
e. 242.95
4. The base of a solid is the region enclosed by the graph of x^2 + 4y^2 = 4 and crosssections perpendicular to the xaxis 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
5. Find the volume of the solid formed by rotating the graph x^2 + 4y^2 = 4 about the xaxis.
a. 8/3
b. 8 pi/3
c. 16/3
d. 32/3
e. 32 pi/3

I will do the first two for you
1. Vol = pi(integral) y^2 by dx from 0 to 4
= pi (integral) (1 + 2x^1/2 + x)dx from 0 to 4
= pi[x + (4/3)x^3/2 + (1/2)x] from 0 to 4
= pi[4 + 32/3 + 8  0]
=71.209
2. from your y = 1 + √x you will need x^2 since you are rotating about the y=axis
y1 = √x
(y1)^4 = x^2
vol = pi (integral) (y1)^4 dy from 1 to 3
= pi[1/5(y1)^5] from 1 to 3
= pi/5( 32  0]
= 20.106 
How about the last one?
#5.
You have an ellipse rotated about the xaxis
the vertices are (2,0) and (2,0)
so because of the symmetry I will find the volume from x=0 to x=2 and double it.
from the equation x^2 = x^2 /4 + 1
so volume = 2pi(integral)((x^2)/4 + x)dx from 0 to 2
= 2pi[(1/12)x^3 + x] from 0 to 2
= 2pi[ 8/12 + 2  0]
= (8/3)pi 
13242
Respond to this Question
Similar Questions

Integral calculus
Please can anyone help with the following problems  thanks. 1) Integrate X^4 e^x dx 2) Integrate Cos^5(x) dx 3) Integrate Cos^n(x) dx 4) Integrate e^(ax)Sinbx dx 5) Integrate 5xCos3x dx The standard way to solve most of these integrals … 
Calculus
Evaluate the triple integral _E (xy)dV where E is a solid tetrahedron with vertices (0,0,0), (4,0,0), (0,1,0), (0,0,4) I just can't seem to find the limits, of x,y and z 
calculus
How do I integrate x(arctanx) dx? Is it some sort of integration by parts? 
Calculus please help!!! double integral
Combine the following two integrals into one by sketching the region, then switching the order of integration. (sketch the region) im gonna use the S for integral sign..because idk what else to use. SS6ycos(x^33x)dxdy+SS6ycos(x^33x) … 
Calculus
Let R be the region bounded by the curve x=9yy^2 and the y axis. Find the volume of the solid resulting from revolving R about the line y= 6. I believe the integral limits are from y=0 to y9 i set up h(x) = 9yy^2 r(x) = y+6 I … 
Integrating Factors
I've been working on this hw problem for a while now, but I'm stuck in the integration process. I'm pretty sure I made an error, cause I can't seem to be able to integrate the right side of the equation. Q: (1/(x^(2)+1))y' + xy = 3 … 
calculus
find the volume of solid inside the paraboloid z=9x^2y^2, outside the cylinder x^2+y^2=4 and above the xyplane 1) solve using double integration of rectangular coordinate. 2) solve using double integration of polar coordinate 3)solve … 
Calculus
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y= 2e^(−x), y= 2, x= 6; about y = 4. How exactly do you set up the integral? 
Cal 2
The region bounded by y=3/(1+x^2), y=0, x=0 and x=3 is rotated about the line x=3. Using cylindrical shells, set up an integral for the volume of the resulting solid. The limits of integration are: 
Calculus II: Finding the volume of a revolution
Question: Find the volume of revolution bounded by yaxis, y=cos(x), and y=sin(x) about the horizontal axis. Since the rotation is happening at the horizontal axis, I thought the limits of integration would be [1,1] and if the curves …