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.
1. Solve for the area between x^3 − 6x^2 + 8x − y = 0 and the x
− axis.
2. Solve for the area bounded by y^2 + x − 4 = 0 and the y −
axis.
3. Solve for the area of the arch of the cycloid x = θ − sinθ, y
= 1 − cosθ.
4. Solve for the area bounded by x^2 − 2x − y = 0 and x^2 − 6x +
y...
The region bounded by y=(1/2)x, y=0, x=2 is rotated around the
x-axis.
A) find the approximation of the volume given by the right
riemann sum with n=1 using the disk method. Sketch the cylinder
that gives approximation of the volume.
B) Fine dthe approximation of the volume by the midpoint riemann
sum with n=2 using disk method. sketch the two cylinders.
Find u(x,y) harmonic in the region in the first quadrant bounded
by y = 0 and y = √3 x such that u(x, 0) = 13 for all x and u(x,y) =
7 if y = √3 x . Express your answer in a form appropriate for a
real variable problem.