Consider the region bounded by cos(x2) and the x−axis for 0 ≤ x
≤ ?(π/2)^1/2 ....
Consider the region bounded by cos(x2) and the x−axis for 0 ≤ x
≤ ?(π/2)^1/2 . If this region is revolved about the y-axis, find
the volume of the solid of revolution. (Note that ONLY the shell
method works here).
The function F(x) = x2 - cos(π x) is defined on the
interval 0 ≤ x ≤ 1 radians. Explain how the Intermediate Value
Theorem shows that F(x) = 0 has a solution on the interval 0 < x
< .
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.
Consider a region R bounded by the y-axis, the line
segment y=8-x for x from 0 to 8, and part of the circle
y=-sqrt(64-x^2) for x from 0 to 8. Find the centroid.
let R be a region bounded by x = 0 and x =1 and y = 0 and y = 1.
Suppose the density is given by 1/y+1.Notice that R is denser
near the x axis. As a result we might
expect the centre of mass to be below the geometric
center(1/2,1/2). Also since the density does not depend on x we do
expect moment of inertia about the x axis to be 1/2. verify the
moment of inertia about...
Consider the region illustrated below, bounded above by ? = ?(?)
= 10 cos ( ?? 9 ) and below by ? = ?(?) = ? −?+3 . The curves
intersect at the points (?, ?(?)) and (?, ?(?)), where 0 < ?
< ? < 5. Do not try to find or estimate the values of ? or
?.
a. The total area of the region.
b. The volume of the solid that has this region as its base,...
1. Consider the region bounded by the graph of y^2 = r^2
−x^2
(a) When this region is rotated about the x-axis a sphere of
radius r is generated. Use integration to find its volume V (b) Use
integration to find the surface area of such a sphere
2. Find the arc length of the curve y = 1 3 x 3/2 on [0, 60]
(
3. Consider the graph of y = x^3 . Compute the surface area of...
Consider the parametric equation of a curve:
x=cos(t), y= 1- sin(t), 0 ≤ t ≤ π
Part (a): Find the Cartesian equation of the
curve by eliminating the parameter. Also, graph the curve and
indicate with an arrow the direction in which the curve is traced
as the parameter increases. Label any x and y intercepts.
Part(b): Find the point (x,y) on the curve with
tangent slope 1 and write the equation of the tangent line.