Pregunta: 1. Using double integration, find the area of the region outside r = 12 and inside r = sin (2θ).

1. Using double integration, find the area of the region outside r = 12 and inside r = sin (2θ).

2. Express the Integral f (x, y, z) dV in 6 continuous ink forms, when E is the solid bounded by E x = 0, y = 0, z = 0, y + z = 1, x + z = 1. I express the integration limits in 6 different ways.

3. Let the solid dotted by the planes x = y2, z = 0, x + z = 1, then

xyzdV AND

4. Express the integral that represents the Volume of the solid bounded by z = x2 + y2, z = 0, x2 + y2 = 4 in polar coordinates.

5. Evaluate √ 1 dV where E is the solid that is inside the cylinder x2 + y2 = 1 and by x2 + y2 above the cone z = 2 x2 + y2 and below the plane z = 2.