Questions from General Calculus

Q: Evaluate the integral where max {x2, y2} means the

Evaluate the integral where max {x2, y2} means the larger of the numbers x2 and y2.

Q: Use cylindrical coordinates. Evaluate ∭E (x + y

Use cylindrical coordinates. Evaluate ∭E (x + y + z) dV, where E is the solid in the first octant that lies under the paraboloid z = 4 - x2 - y2.

Q: Plot the point whose cylindrical coordinates are given. Then find the

Plot the point whose cylindrical coordinates are given. Then find the rectangular coordinates of the point. (a). (√(2 ), 3π/4, 2) (b). (1, 1, 1)

Q: Use cylindrical coordinates. Evaluate ∭E (x – y

Use cylindrical coordinates. Evaluate ∭E (x – y) dV, where E is the solid that lies between the cylinders x2 + y2 = 1 and x2 + y2 = 16, above the xy-plane, and below the plane z = y + 4.

Q: Use cylindrical coordinates. Evaluate ∭E x2 dV, where

Use cylindrical coordinates. Evaluate ∭E x2 dV, where E is the solid that lies within the cylinder x2 + y2 = 1, above the plane z = 0, and below the cone z2 = 4x2 + 4y2.

Q: Use cylindrical coordinates. Find the volume of the solid that

Use cylindrical coordinates. Find the volume of the solid that lies within both the cylinder x2 + y2 = 1 and the sphere x2 + y2 + z2 = 4.

Q: Use cylindrical coordinates. Find the volume of the solid that

Use cylindrical coordinates. Find the volume of the solid that is enclosed by the cone z = √(x^2 + y^2 ) and the sphere x2 + y2 + z2 = 2.

Q: Use cylindrical coordinates. Find the volume of the solid that

Use cylindrical coordinates. Find the volume of the solid that lies between the paraboloid z = x2 + y2 and the sphere x2 + y2 + z2 = 2.

Q: Use the Midpoint Rule for triple integrals (Exercise 24) to

Use the Midpoint Rule for triple integrals (Exercise 24) to estimate the value of the integral. Divide B into eight sub-boxes of equal size. ∭B cos (xyz) dV, where B = {(x, y, z) | 0 < x < 1, 0 < y <...

Q: Use the Midpoint Rule for triple integrals (Exercise 24) to

Use the Midpoint Rule for triple integrals (Exercise 24) to estimate the value of the integral. Divide B into eight sub-boxes of equal size. ∭B √x e xyz dV, where B = {(x, y, z) | 0 < x < 4, 0 < y < 1...