Questions from General Calculus

Q: Sketch the region of integration and change the order of integration.

Sketch the region of integration and change the order of integration. ∫_1^2 ∫_0^lnxf (x,y) dy dx

Q: Find the mass and center of mass of the lamina that occupies

Find the mass and center of mass of the lamina that occupies the region D and has the given density function ρ. D is the triangular region with vertices (0, 0), (2, 1), (0, 3); ρ (x, y) = x + y

Q: Sketch the region of integration and change the order of integration.

Sketch the region of integration and change the order of integration. ∫_0^1 ∫_arctanx^(π/4) f (x,y) dy dx

Q: Evaluate the integral by reversing the order of integration. ∫_

Evaluate the integral by reversing the order of integration. ∫_0^1 ∫_(x^2)^1√y sin y dy dx

Q: Evaluate the integral by reversing the order of integration. ∫_

Evaluate the integral by reversing the order of integration. ∫_0^1 ∫_(√x)^1√(y^3+1) dy dx

Q: Evaluate the integral by reversing the order of integration. ∫_

Evaluate the integral by reversing the order of integration. ∫_0^2 ∫_(y/2)^1y cos (x3 – 1) dx dy

Q: Find the area of the surface. The part of the

Find the area of the surface. The part of the cylinder x2 + z2 = 4 that lies above the square with vertices (0, 0), (1, 0), (0, 1), and (1, 1)

Q: Find the area of the surface. The part of the

Find the area of the surface. The part of the hyperbolic paraboloid z = y2 - x2 that lies between the cylinders x2 + y2 = 1 and x2 + y2 = 4

Q: If the ellipse x2/a2 + y2/b2 = 1

If the ellipse x2/a2 + y2/b2 = 1 is to enclose the circle x2 + y2 = 2y, what values of a and b minimize the area of the ellipse?

Q: Find the area of the surface. The surface z =

Find the area of the surface. The surface z =2/3 (x3/2 + y3/2), 0 < x < 1, 0 < y < 1