Find the volume of the solid obtained by revolving the region
bounded above by the curve y = f(x) and below by the curve y= g(x)
from x = a to x = b about the x-axis.
f(x) = 3 − x2 and g(x) = 2; a =
−1, b = 1
Find the volume of the solid of revolution that is formed by
rotating the region bounded by the graphs of the equations given
around the indicated line or axis
1.- y=9-x^2, y=0, around the x axis
2.- y=√x-1, x=5, y=0, around the x=5
3.- y=1-x, x=0, y=0, around the y= -2
4.- y=x^2, x=0, y=3, around the y axis
a)
Find the volume of the solid obtained by revolving the region in
the first quadrant bounded by the curves y= x^(1/2) & y= x^5
about the x-axis
b) Find the volume of the solid obtained by revolving the
region between the curve
f(x)= x^(1/3) , the line y=2, and the line x=8 about the
y-axis
Find the volume of the solid generated by revolving the region
bounded by y = sqrt(x) and the lines and y=2 and x=0 about:
1) the x-axis.
2) the y-axis.
3) the line y=2.
4) the line x=4.
Find the volume of the solid obtained by rotating the region
bounded by y = x 3 , y = 1, x = 2 about the line y = −3.
Sketch the region, the solid, and a typical disk or washer
(cross section in xy-plane).
Show all the work and explain thoroughly.
a.)Using disks or washers, find the volume of the solid obtained
by rotating the region bounded by the curves y^2=x and x = 2y about
the y-axis
b.) Find the volume of the solid that results when the region
bounded by x=y^2 and x=2y+15 is revolved about the y-axis
c.) Find the length of the curve y=ln(x) ,1≤x≤sqrt(3)
d.)Consider the curve defined by the equation xy=5. Set up an
integral to find the length of curve from x=a to x=b