91Ó°ÊÓ

Find the volume \(V\) of the region, using the methods of this section. The region bounded above by the plane \(z=10+2 x+3 y\), below by the \(x y\) plane, and on the sides by the surfaces \(y=x^{2}\) and \(y=x\)

The iterated integral represents the volume of a solid region \(D .\) Sketch the region \(D\). $$ \int_{-3}^{3} \int_{-\sqrt{9-x^{2}}}^{\sqrt{9-x^{2}}} 5 d y d x $$

The iterated integral represents the volume of a solid region \(D .\) Sketch the region \(D\). $$ \int_{-5}^{5} \int_{-\sqrt{25-x^{2}}}^{\sqrt{25-x^{2}}} \sqrt{25-x^{2}-y^{2}} d y d x $$

The iterated integral represents the volume of a solid region \(D .\) Sketch the region \(D\). $$ \int_{0}^{5} \int_{0}^{\sqrt{25-x^{2}}} \sqrt{25-x^{2}-y^{2}} d y d x $$

Find the area \(A\) of the region in the \(x y\) plane by the methods of this section. The region bounded by the parabolas \(y=x^{2}\) and \(y=\sqrt{x}\) on \([1,4]\)

Find the area \(A\) of the region in the \(x y\) plane by the methods of this section. The region bounded by the graphs of the equations \(y=\cosh x\) and \(y=\sinh x\) on \([-1,1]\) (Leave your answer in terms of cosh or sinh.)

Find the area \(A\) of the region in the \(x y\) plane by the methods of this section. The region between the parabolas \(x=y^{2}\) and \(x=32-y^{2}\)

Find the area \(A\) of the region in the \(x y\) plane by the methods of this section. The region bounded by the parabolas \(x=y^{2}\) and \(x=4 y^{2}-3\)

Find the area \(A\) of the region in the \(x y\) plane by the methods of this section. The region in the first quadrant that is bounded by the graph of \(x=2-y^{2}\) and by the lines \(x=0\) and \(x=y\)

Find the area \(A\) of the region in the \(x y\) plane by the methods of this section. The region in the first quadrant that is bounded by the graphs of \(x+y=4\) and \(y=3 / x\)