Question

volume bounded by xy plane,the cylinder (x^2+y^2=1)and the plane (x+y+z=1)

Answer 1

\[\int_0^{2\pi} r (-r \sin (\theta )-r \cos
(\theta )+1)d\theta=2\pi r\]

Answer 2

\[x = r \cos(\theta)
\\
y = r \sin(\theta)\\

dV= r dr d\theta\\

\int_o^1\int_0^{2\pi} r (-r \sin (\theta )-r \cos
(\theta )+1)d\theta dr=\\
\int_o^1 2 r \pi dr=\pi
\]