Solve the problem.
-Find the mass of a thin circular plate bounded by $x ^ { 2 } + y ^ { 2 } = 4$ if $\delta ( x , y ) = x ^ { 2 } + y ^ { 2 }$.
A) $8 \pi$
B) $2 \pi$
C) $1 \pi$
D) $4 \pi$

Question

Quizplus · Accepted Answer

The mass of the plate is given by the integral of the density function over the region. The density function $\delta(x, y) = x^2 + y^2$ is equal to $r^2$ in polar coordinates. The region is a circle of radius 2, so the integral becomes $\int_0^{2\pi} \int_0^2 r^3 \, dr \, d\theta$. Evaluating this integral gives $8\pi$.

Solve the Problem x2+y2=4x ^ { 2 } + y ^ { 2 } = 4x2+y2=4

Solve the Problem $x ^ { 2 } + y ^ { 2 } = 4$