Questions from General Calculus

Q: Set up, but do not evaluate, an integral for the

Set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

Q: Find the volumes of the solids obtained by rotating the region bounded

Find the volumes of the solids obtained by rotating the region bounded by the curves y = x and y = x2 about the following lines. (a) The x-axis (b) The y-axis (c) y = 2

Q: Let / be the region in the first quadrant bounded by the

Let / be the region in the first quadrant bounded by the curves y = x3 and y = 2x 2 x2. Calculate the following quantities. (a) The area of / (b) The volume obtained by rotating / about the x-axis (c...

Q: Let / be the region bounded by the curves y = tan

Let / be the region bounded by the curves y = tan(x2), x = 1, and y = 0. Use the Midpoint Rule with n = 4 to estimate the following quantities. (a) The area of/ b) The volume obtained by rotating / ab...

Q: Let / be the region bounded by the curves y = 1

Let / be the region bounded by the curves y = 1 - x2 and y = x6 - x + 1. Estimate the following quantities. (a) The x-coordinates of the points of intersection of the curves (b) The area of / (c) The...

Q: Each integral represents the volume of a solid. Describe the solid

Each integral represents the volume of a solid. Describe the solid.

Q: Each integral represents the volume of a solid. Describe the solid

Each integral represents the volume of a solid. Describe the solid.

Q: Sketch the region enclosed by the given curves and find its area

Sketch the region enclosed by the given curves and find its area.

Q: The base of a solid is a circular disk with radius 3

The base of a solid is a circular disk with radius 3. Find the volume of the solid if parallel cross-sections perpendicular to the base are isosceles right triangles with hypotenuse lying along the ba...

Q: The base of a solid is the region bounded by the parabolas

The base of a solid is the region bounded by the parabolas y = x2 and y = 2 - x2. Find the volume of the solid if the cross-sections perpendicular to the x-axis are squares with one side lying along t...