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Question

asked 2021-05-26

Evaluate the surface integral.

\(\int \int_s (x^2z +y^2z)dS\)

S is the hemisphere \(x^2 +y^2 + z^2 = 9, z \geq 0\)

\(\int \int_s (x^2z +y^2z)dS\)

S is the hemisphere \(x^2 +y^2 + z^2 = 9, z \geq 0\)

asked 2021-05-26

Calculate the double integral \(\frac{6x}{1+xy}dA , R=\left[0,6\right] \times \left[0,1\right]\)

asked 2021-05-12

Calculate the double integral.

\(\int \int_R \frac{4x}{1+xy}dA\)

\(R=\left[0,4\right] \times \left[0,1\right]\)

\(\int \int_R \frac{4x}{1+xy}dA\)

\(R=\left[0,4\right] \times \left[0,1\right]\)

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.