Questions from General Calculus

Q: Find the volume of the solid by subtracting two volumes.

Find the volume of the solid by subtracting two volumes. The solid enclosed by the parabolic cylinders y = 1 - x2, y = x2 - 1 and the planes x + y + z = 2, 2x + 2y – z+1 10 = 0

Q: Evaluate the integral by changing to spherical coordinates ∫_0^

Evaluate the integral by changing to spherical coordinates ∫_0^1 ∫_0^(√(1-x^2 )) ∫_(√(x^2+y^2 ))^(√(2-x^2-y^2 )) xy dz dy dx

Q: Sketch the solid whose volume is given by the iterated integral.

Sketch the solid whose volume is given by the iterated integral. ∫_0^1 ∫_0^1(4 - x - 2y) dx dy

Q: Find the volume of the solid enclosed by the paraboloid z =

Find the volume of the solid enclosed by the paraboloid z = 2 + x2 + (y – 2)2 and the planes z = 1, x = 1, x = 21, y = 0, and y = 4.

Q: Use a computer algebra system to find the exact volume of the

Use a computer algebra system to find the exact volume of the solid. Enclosed by z = x2 + y2 and z = 2y

Q: Use a graphing device to draw a silo consisting of a cylinder

Use a graphing device to draw a silo consisting of a cylinder with radius 3 and height 10 surmounted by a hemisphere.

Q: Graph the solid that lies between the surface z = 2xy/

Graph the solid that lies between the surface z = 2xy/ (x2 + 1) and the plane z = x + 2y and is bounded by the planes x = 0, x = 2, y = 0, and y = 4. Then find its volume.

Q: (a). A cylindrical drill with radius r1 is used to

(a). A cylindrical drill with radius r1 is used to bore a hole through the center of a sphere of radius r2. Find the volume of the ring-shaped solid that remains. (b). Express the volume in part (a) i...

Q: (a). Use cylindrical coordinates to show that the volume of

(a). Use cylindrical coordinates to show that the volume of the solid bounded above by the sphere r2 + z2 = a2 and below by the cone z = r cot φ0 (or φ = φ0), where 0...

Q: Set up iterated integrals for both orders of integration. Then evaluate

Set up iterated integrals for both orders of integration. Then evaluate the double integral using the easier order and explain why it’s easier. ∬D y dA, D is bounded by y = x - 2, x = y2