i have a calc test tomorrow and i can't solve these practice problems. help please!!!
Compute the following definite integrals:
(a) integral from -1 to 1 of sin(x)sin(x^2)dx
(b) integral from 0 to pi of cos(x) / (2 + sin(x)^2
Given two curves y^2 - x = 0 and x + 2y = 3
(a) Find the area of the region bounded between the curves
(b) Find the centroid of the region
(c) Find the volume of the solid obtained by revolving the region around the y-axis
Consider a region with area equal to A lying in some plant. Consider a point P at a height h above the plane. Consider the solid 'cone' formed by joining P to all points of the region by line segments. Show that the volume of this solid is Ah/3. (Hint: Use the face that if you scale a region so that the distances get multiplied by a factor k, then the areas get scaled by the factor k^2.)
Use the shell method to find the volume enclosed by the surface obtained by revolving the ellipse x^2/a^2 + y^2/b^2 = 1 about the y-axis.
Let f(x) = xe^(-x^2/2)
(a) On what intervals does f increase? Decrease?
(b) Find the extreme values of f.
(c) Determine the concavity of the graph and find the points of inflection.
(d) Sketch the graph indicating the asymptotes if any
A 13-foot ladder is leaning against a vertical wall. If the bottom of the ladder is being pulled away from the wall at the rate of 2 feet per second, how fast is the area of the triangle formed by the wall, the ground, and the ladder changing when the bottom of the ladder is 12 feet from the wall? How fast is the top of the ladder dropping?
any help at all is very very very much appreciated!