Volume with Cross Sections
This is the setup for the volume of the solid generated by creating cross sections of squares perpendicular to the x-axis for the region:
y=cos(x), -\pi/2<=x<=\pi/2
What is
\int_(-\pi/2)^(\pi/2)[cos(x)]^2dx?
This is the volume of the solid generated by revolving the region bounded by the following curves about the y-axis:
y=9x, y=1, and y=5
What is
(124\pi)/243 or 1.603?
Find the area bounded by f(x)=x^2-4x+3 and g(x)=2x-x^2
What is 1.732?
This is the volume of the solid generated by revolving the region bounded by the following curves about the x-axis:
y=-x^2+6 and y=2
What is
(384\pi)/5 or 241.274?
This is the setup for the volume of the solid generated by revolving the region bounded by the following curves about the line y = 2:
y=x^2-3 and y=\sqrt(x)-3
What is
\pi\int_0^1(5-x^2)^2-(5-\sqrt(x))^2dx?
This is the setup for the volume of the solid generated by creating cross sections of semi-circles perpendicular to the y-axis for the region:
x=\sqrt(16-y^2)
What is
\int_-4^4\pi/8[\sqrt(16-y^2)]^2dy?
This is the volume of the solid generated by revolving the region bounded by the following curves about the x-axis:
y=9x+2, x=2, and x=6
What is
6208pi or 19503.007?
Consider the region enclosed by x=y^2-1 and y=(x-3)/2 . Find the area of this region.
What is 14.907?
This is the volume of the solid generated by revolving the region bounded by the following curves about the y-axis:
y=x^2 and x=2y
What is
\pi/96 or 0.033?
This is the setup for the volume of the solid generated by revolving the region bounded by the following curves about the line x = 1:
x=-y^2+5, x=1, y=0, and y=2
What is
\pi\int_0^2(-y^2+4)^2dy?
This is the setup for the volume of the solid whose base is in the first quadrant and is generated by creating cross sections of isosceles right triangles perpendicular to the x-axis for the region:
y=2-x
What is
\int_0^2 1/2(2-x)^2dx?
This is the volume of the solid generated by revolving the region bounded by the following curves about the x-axis:
y=x\sqrt(2-x) and y=0
What is
(4\pi)/3 or 4.189?
Let f(x)=x^3-4x+2 and g(x)=-1/2x . Find the area bounded by the functions.
What is 7.941?
This is the volume of the solid generated by revolving the region bounded by the following curves about the x-axis:
y=-x^2+4, y=x^2+2, x=0, and x=-1
What is
8\pi or 25.133?
This is the setup for the volume of the solid generated by revolving the region bounded by the following curves about the line y = -1:
y=x^2+4, y=2, x=0, and x=1
What is
\pi\int_0^1(x^2+5)^2-(3)^2dx?
This is the setup for the volume of the solid generated by creating cross sections of equilateral triangles perpendicular to the y-axis for the region in Q1:
y=-x^2+9
What is
\int_0^9 \sqrt3/4[\sqrt(-y+9)]^2dy?
This is the volume of the solid generated by revolving the region bounded by the following curves about the y-axis:
y=ln(x), y=0, and y=ln(7)
What is
24\pi or 75.398?
Let f(x)=sqrt(x+1) .
Let L(x) be the line tangent to f(x) at x=3.
Find the area enclosed by L(x) and f(x)
What is 0?
This is the volume of the solid generated by revolving the region bounded by the following curves about the y-axis:
y=\sqrt(-x+3) and x=2
What is
(16\pi)/5 or 10.053?
This is the setup for the volume of the solid generated by revolving the region bounded by the following curves about the line x = 3:
y=\sqrt(-x-1), x=-2, y=0, and y=1
What is
\pi\int_0^1(5)^2-(-y^2+4)^2dy?