Questions from General Calculus

Q: Calculate the double integral. ∬R 1/(1+

Calculate the double integral. ∬R 1/(1+ x+ y) dA, R = [1, 3] × [1, 2]

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

Find the volume of the solid by subtracting two volumes. The solid in the first octant under the plane z = x + y, above the surface z = xy, and enclosed by the surfaces x = 0, y = 0, and x2 + y2 = 4

Q: Find the volume of the solid lying under the elliptic paraboloid x2

Find the volume of the solid lying under the elliptic paraboloid x2/4 + y2/9 + z = 1 and above the rectangle R = [-1, 1] × [-2, 2].

Q: Evaluate the iterated integral. ∫_0^(π/2

Evaluate the iterated integral. ∫_0^(π/2) ∫_0^x〖(x siny)〗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-x^2) (1 - x) dy dx

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. Under the surface z = x3y4 + xy2 and above the region bounded by the curves y = x3 - x and y = x2 + x for x > 0

Q: Evaluate the iterated integral. ∫_0^1 ∫_0

Evaluate the iterated integral. ∫_0^1 ∫_0^(x^2)cos (s^3) dt ds

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 55 14.7 Exercise 55: If the length of the diagonal of a rectangular box must be L, what is...

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

Evaluate the double integral. ∬D (2x + y) dA, D = {(x, y) | 1 < y < 2, y - 1 < x < 1}

Q: Evaluate the double integral. ∬D e^(-y^

Evaluate the double integral. ∬D e^(-y^2 ) dA, D = {(x, y) | 0 < y < 3, 0 < x < y}