91Ó°ÊÓ

Sketch the region of integration, reverse the order of integration, and evaluate the integral. $$\int_{0}^{8} \int_{\sqrt{x}}^{2} \frac{d y d x}{y^{4}+1}$$

Find the volume of the region bounded below by the paraboloid \(z=x^{2}+y^{2},\) laterally by the cylinder \(x^{2}+y^{2}=1,\) and above by the paraboloid \(z=\) \(x^{2}+y^{2}+1\).

Find the volume of the region bounded below by the paraboloid \(z=x^{2}+y^{2},\) laterally by the cylinder \(x^{2}+y^{2}=1,\) and above by the paraboloid \(z=\) \(x^{2}+y^{2}+1\).

Sketch the region of integration, reverse the order of integration, and evaluate the integral. Square region \(\iint_{R}\left(y-2 x^{2}\right) d A\) where \(R\) is the region bounded by the square \(|x|+|y|=1\)

Find the volume of the region that lies inside the sphere \(x^{2}+y^{2}+z^{2}=2\) and outside the cylinder \(x^{2}+y^{2}=1\).

Sketch the region of integration, reverse the order of integration, and evaluate the integral. Triangular region \(\iint_{R} x y d A\) where \(R\) is the region bounded by the lines \(y=x, y=2 x,\) and \(x+y=2\)

Find the volume of the region enclosed by the cylinder \(x^{2}+y^{2}=4\) and the planes \(z=0\) and \(y+z=4\).

Find the volume of the region bounded above by the paraboloid \(z=x^{2}+y^{2}\) and below by the triangle enclosed by the lines \(y=x, x=0,\) and \(x+y=2\) in the \(x y\) -plane.

Find the volume of the region enclosed by the cylinder \(x^{2}+y^{2}=4\) and the planes \(z=0\) and \(x+y+z=4\).

Sketch the region of integration, reverse the order of integration, and evaluate the integral. Find the volume of the solid that is bounded above by the cylinder \(z=x^{2}\) and below by the region enclosed by the parabola \(y=2-x^{2}\) and the line \(y=x\) in the \(x y\) -plane.