Questions from General Calculus

Q: (a). Estimate the volume of the solid that lies below

(a). Estimate the volume of the solid that lies below the surface z = xy and above the rectangle R = {(x, y) | 0 < x < 6, 0 < y < 4} Use a Riemann sum with m = 3, n = 2, and take the sample point to...

Q: The integral ∬R √(9 - y^2 ) dA

The integral ∬R √(9 - y^2 ) dA, where R = [0, 4] × [0, 2], represents the volume of a solid. Sketch the solid.

Q: Find ∫_0^2 f (x,y) dx

Find ∫_0^2 f (x,y) dx and ∫_0^3 f(x,y) dy f (x, y) = y√(x + 2)

Q: Evaluate the double integral. ∬D y2 dA, D

Evaluate the double integral. ∬D y2 dA, D is the triangular region with vertices (0, 1), (1, 2), (4, 1)

Q: Evaluate the iterated integral. ∫_0^2 ∫_0

Evaluate the iterated integral. ∫_0^2 ∫_0^2(x^2 y dx dy

Q: Evaluate the double integral. ∬D y2 dA, D

Evaluate the double integral. ∬D y2 dA, D is enclosed by the quarter-circle y = √(1 -x^2 ), x > 0, and the axes

Q: Use Lagrange multipliers to give an alternate solution to the indicated exercise

Use Lagrange multipliers to give an alternate solution to the indicated exercise in Section 14.7. Exercise 51 14.7 Exercise 51: Find the dimensions of a rectangular box of maximum volume such that t...

Q: Evaluate the double integral. ∬D y dA, D

Evaluate the double integral. ∬D y dA, D is the triangular region with vertices (0, 0), (1, 1), and (4, 0)

Q: Find the volume of the given solid. Under the plane

Find the volume of the given solid. Under the plane 3x + 2y - z = 0 and above the region enclosed by the parabolas y = x2 and x = y2

Q: Find the volume of the given solid. Under the surface

Find the volume of the given solid. Under the surface z = 1 + x2y2 and above the region enclosed by x = y2 and x = 4