Questions from General Calculus

Q: Calculate the value of the multiple integral. ∬E xy

Calculate the value of the multiple integral. ∬E xy dV, where E = {(x, y, z) | 0 < x < 3, 0 < y < x, 0 < z < x + y}

Q: Calculate the value of the multiple integral. ∭T xy

Calculate the value of the multiple integral. ∭T xy dV, where T is the solid tetrahedron with vertices (0, 0, 0), (1/3 , 0, 0), (0, 1, 0), and (0, 0, 1)

Q: Calculate the value of the multiple integral. ∭E y2z2

Calculate the value of the multiple integral. ∭E y2z2 dV, where E is bounded by the paraboloid x = 1 - y2 - z2 and the plane x = 0

Q: Calculate the value of the multiple integral. ∭H z3

Calculate the value of the multiple integral. ∭H z3√(x^2+y^2+ z^2 ) dV, where H is the solid hemisphere that lies above the xy-plane and has center the origin and radius 1

Q: Find the gradient of the function f (x, y,

Find the gradient of the function f (x, y, z) = x2eyz2.

Q: Find the area of the part of the cone z2 = a2

Find the area of the part of the cone z2 = a2(x2 + y2) between the planes z = 1 and z = 2.

Q: Find the directional derivative of f at the given point in the

Find the directional derivative of f at the given point in the indicated direction. f (x, y) = x2e-y, (-2, 0), in the direction toward the point (2, -3)

Q: If D is the region bounded by the curves y = 1

If D is the region bounded by the curves y = 1/2 x2 and y = ex, find the approximate value of the integral ∬D y2 dA. (Use a graphing device to estimate the points of intersection of the curves.)

Q: Describe the region whose area is given by the integral ∫_

Describe the region whose area is given by the integral ∫_0^(π/2) ∫_0^sin2θr dr dθ

Q: (a). A lamp has two bulbs, each of a

(a). A lamp has two bulbs, each of a type with average lifetime 1000 hours. Assuming that we can model the probability of failure of a bulb by an exponential density function with mean μ = 1000, find...