22. find the area of the surface generated by revolving the
parametric curve about the y-axis.
x = 2 sin t + 1 , y = 2 cos t + 5 , (0) less than or equal to
(t) less than or equal to (pi/4)
Find the area between the curve and the x-axis over the
indicated interval.
y = 100 − x2;
[−10,10]
The area under the curve is ___
(Simplify your answer.)
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.
If the infinite curve y = e−3x, x ≥ 0, is rotated about the
x-axis, find the area of the resulting surface. (answer needs to be
in fraction form if possible)