a) Find the area of the region bounded by the line y = x and the
curve y = 2 - x^2. Include a sketch.
Find the volume of the solid created when rotating the region in
part a) about the line x = 1, in two ways.
A. Find the region bounded by the curves y = (x−3)^2 and y =
12−4x. Show all of your work.
B. Find the equation of the tangent line to the curve 5x^2 −6xy
+ 5y^2 = 4 at the point (1,1) Show all of your work. Thanks
1.
Find the volume of the region bounded by
y = ln(x), y = 1, y = 2,
x = 0
and rotated about the y-axis. Which method will be
easier for this problem?
2.
Find the volume of the region bounded by
y = 2x + 2, x =
y2-2y
and rotated about y = 2. Which method will be easier
for this problem? NOTE: You do
not need to integrate this problem, just set it up.
9) R is the region bounded by the curves ? = x^3 , y=2x+4 , And
the y-axis.
a) Find the area of the region.
b) Set up the integral you would use to find the volume of a
solid that has R as the base and square cross sections
perpendicular to the x-axis.