Questions from General Calculus

Q: Evaluate the double integral. ∬D (x2 + 2y

Evaluate the double integral. ∬D (x2 + 2y) dA, D is bounded by y = x, y = x3, x > 0

Q: A region R is shown. Decide whether to use polar coordinates

A region R is shown. Decide whether to use polar coordinates or rectangular coordinates and write ∬R f (x, y) dA as an iterated integral, where f is an arbitrary continuous function o...

Q: Use polar coordinates to find the volume of the given solid.

Use polar coordinates to find the volume of the given solid. Below the plane 2x + y + z = 4 and above the disk x2 + y2 < 1

Q: Use polar coordinates to find the volume of the given solid.

Use polar coordinates to find the volume of the given solid. Inside the sphere x2 + y2 + z2 = 16 and outside the cylinder x2 + y2 = 4

Q: Use polar coordinates to find the volume of the given solid.

Use polar coordinates to find the volume of the given solid. A sphere of radius a

Q: Use polar coordinates to find the volume of the given solid.

Use polar coordinates to find the volume of the given solid. Bounded by the paraboloid z = 1 + 2x2 + 2y2 and the plane z = 7 in the first octant

Q: Use polar coordinates to find the volume of the given solid.

Use polar coordinates to find the volume of the given solid. Above the cone z = √(x^2 + y^2 ) and below the sphere x2 + y2 + z2 = 1

Q: Use polar coordinates to find the volume of the given solid.

Use polar coordinates to find the volume of the given solid. Bounded by the paraboloids z = 6 - x2 - y2 and z = 2x2 + 2y2

Q: The plane x + y + 2z = 2 intersects the paraboloid

The plane x + y + 2z = 2 intersects the paraboloid z = x2 + y2 in an ellipse. Find the points on this ellipse that are nearest to and farthest from the origin.

Q: A region R is shown. Decide whether to use polar coordinates

A region R is shown. Decide whether to use polar coordinates or rectangular coordinates and write ∬R f (x, y) dA as an iterated integral, where f is an arbitrary continuous function o...