Find the volume of the solid by subtracting two volumes, the
solid enclosed by the parabolic cylinders y = 1 − x2, y = x2 − 1
and the planes x + y + z = 2, 3x + 3y − z + 15 = 0.
a. Find the volume of the solid obtained by rotating the region
enclosed by the curves y = 4 x^2 , y = 5 − x^2 about the line y =
11
b. Find the volume of the solid obtained by rotating the region
enclosed by the graphs about the given axis.
y = 2sqt (x), y=x, about x=-20.
Please leave your answer in fraction if
possble
Answer the following questions:
Part A: Volumes of Revolution
a) Find the volume of the solid obtained when the region bounded
by y = 1/x , and the lines x = 1, x = 3 and y = 0 is rotated about
the x-axis.
b) Find the volume of the solid obtained by revolving the region
bounded by the parabolas y = x^2 and y^2 = 8x about the x-axis.
c) Find the volume of the solid obtained by revolving...
1-Find the volume of the solid formed by rotating the region
enclosed by
y=e^1x+2, y=0, x=0, x=0.7
about the y-axis.
2-Use cylindrical shells to find the volume of the solid formed
by rotating the area between the graph of x=y^9/2 andx=0,0≤y≤1
about the x-axis.
Volume = ∫10f(y)dy∫01f(y)dy where, find the f(y) and the voume.
3- x=y^5/2 andx=0,0≤y≤1 about the line y = 2 to find the volume
and the f(y) by the cylindrical shells
Find the volume of the solid using triple integrals. The solid
bounded below by the cone
z= sqr
x2+y2 and bounded above by the sphere
x2+y2+z2=8.(Figure)
Find and sketch the region of integration R.
Setup the triple integral in Cartesian coordinates.
Setup the triple integral in Spherical coordinates.
Setup the triple integral in Cylindrical coordinates.
Evaluate the triple integral in Cylindrical coordinates.