Question

asked 2021-06-06

Use a double integral to find the area of the region. The region inside the circle \((x - 5)^2 + y^2 = 25\) and outside the circle \(x^2 + y^2 = 25\)

asked 2021-05-17

The integral represents the volume of a solid. Describe the solid.

\(\pi\int_{0}^{1}(y^{4}-y^{8})dy\)

a) The integral describes the volume of the solid obtained by rotating the region \(R=\{\{x,\ y\}|0\leq y\leq1,\ y^{4}\leq x\leq y^{2}\}\) of the xy-plane about the x-axis.

b) The integral describes the volume of the solid obtained by rotating the region \(R=\{\{x,\ y\}|0\leq y\leq1,\ y^{2}\leq x\leq y^{4}\}\) of the xy-plane about the x-axis.

c) The integral describes the volume of the solid obtained by rotating the region \(R=\{\{x,\ y\}|0\leq y\leq1,\ y^{4}\leq x\leq y^{2}\}\) of the xy-plane about the y-axis.

d) The integral describes the volume of the solid obtained by rotating the region \(R=\{\{x,\ y\}|0\leq y\leq1,\ y^{2}\leq x\leq y^{4}\}\) of the xy-plane about the y-axis.

e) The integral describes the volume of the solid obtained by rotating the region \(R=\{\{x,\ y\}|0\leq y\leq1,\ y^{4}\leq x\leq y^{8}\}\) of the xy-plane about the y-axis.

\(\pi\int_{0}^{1}(y^{4}-y^{8})dy\)

a) The integral describes the volume of the solid obtained by rotating the region \(R=\{\{x,\ y\}|0\leq y\leq1,\ y^{4}\leq x\leq y^{2}\}\) of the xy-plane about the x-axis.

b) The integral describes the volume of the solid obtained by rotating the region \(R=\{\{x,\ y\}|0\leq y\leq1,\ y^{2}\leq x\leq y^{4}\}\) of the xy-plane about the x-axis.

c) The integral describes the volume of the solid obtained by rotating the region \(R=\{\{x,\ y\}|0\leq y\leq1,\ y^{4}\leq x\leq y^{2}\}\) of the xy-plane about the y-axis.

d) The integral describes the volume of the solid obtained by rotating the region \(R=\{\{x,\ y\}|0\leq y\leq1,\ y^{2}\leq x\leq y^{4}\}\) of the xy-plane about the y-axis.

e) The integral describes the volume of the solid obtained by rotating the region \(R=\{\{x,\ y\}|0\leq y\leq1,\ y^{4}\leq x\leq y^{8}\}\) of the xy-plane about the y-axis.

asked 2021-06-11

Use a double integral to find the area of the region. The region inside the cardioid \(r=1+\cos \theta\) and outside the circle \(r=3 \cos \theta\)

asked 2021-06-08

1) Find the area of the part of the plane

4x + 3y + z = 12

that lies in the first octant.

2) Use polar coordinates to find the volume of the given solid.

Bounded by the paraboloid \(z = 5 + 2x^2 + 2y^2\) and the plane z = 11 in the first octant

4x + 3y + z = 12

that lies in the first octant.

2) Use polar coordinates to find the volume of the given solid.

Bounded by the paraboloid \(z = 5 + 2x^2 + 2y^2\) and the plane z = 11 in the first octant