Questions from General Calculus

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

Evaluate the double integral. ∬D (2x – y) dA, D is bounded by the circle with center the origin and radius 2

Q: Evaluate the double integral. ∬D y/(x^

Evaluate the double integral. ∬D y/(x^2+1) dA, D = {(x, y) | 0 < x < 4, 0 < y < √x}

Q: Sketch the region whose area is given by the integral and evaluate

Sketch the region whose area is given by the integral and evaluate the integral. ∫_(π/4)^(3π/4) ∫_1^2r dr dθ

Q: Electric charge is distributed over the rectangle 0 < x < 5

Electric charge is distributed over the rectangle 0 < x < 5, 2 < y < 5 so that the charge density at (x, y) is σ (x, y) = 2x + 4y (measured in coulombs per square meter). Find the total charge on th...

Q: A lamina with constant density ρ (x, y) =

A lamina with constant density ρ (x, y) = ρ occupies the given region. Find the moments of inertia Ix and Iy and the radii of gyration x and y. The rectangle 0 < x < b, 0 < y < h

Q: A lamina with constant density ρ (x, y) =

A lamina with constant density ρ (x, y) = ρ occupies the given region. Find the moments of inertia Ix and Iy and the radii of gyration x and y. The triangle with vertices (0, 0), (b, 0), and (0, h)

Q: A lamina with constant density ρ (x, y) =

A lamina with constant density ρ (x, y) = ρ occupies the given region. Find the moments of inertia Ix and Iy and the radii of gyration x and y. The part of the disk x2 + y2 < a2 in the first quadrant...

Q: A lamina with constant density ρ (x, y) =

A lamina with constant density ρ (x, y) = ρ occupies the given region. Find the moments of inertia Ix and Iy and the radii of gyration x and y. The region under the curve y = sin x from x = 0 to x = π...

Q: Use a computer algebra system to find the mass, center of

Use a computer algebra system to find the mass, center of mass, and moments of inertia of the lamina that occupies the region D and has the given density function. D = {(x, y) | 0 < y < xe-x, 0 < x <...

Q: Use spherical coordinates. (a). Find the volume of

Use spherical coordinates. (a). Find the volume of the solid that lies above the cone φ = π/3 and below the sphere ρ = 4 cos φ. (b). Find the centroid of the solid in part (a).