The integral represents the volume of a solid. Describe the solid.302𝜋x7 dxThe solid is obtained by rotating the region 0 ≤ y ≤ x6, 0 ≤ x ≤ 3 about the x-axis using cylindrical shells.The solid is obtained by rotating the region 0 ≤ y ≤ x7, 0 ≤ x ≤ 3 about the y-axis using cylindrical shells.    The solid is obtained by rotating the region 0 ≤ y ≤ x7, 0 ≤ x ≤ 3 about the x-axis using cylindrical shells.The solid is obtained by rotating the region 0 ≤ y ≤ x6, 0 ≤ x ≤ 3 about the y-axis using cylindrical shells.The solid is obtained by rotating the region 0 ≤ y ≤ 2𝜋, 0 ≤ x7 ≤ 3 about the y-axis using cylindrical shells.

Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis.xy = 7,  x = 0,  y = 7,  y = 9

Step 2Now we can say that the volume of the solid created by rotating the region under y = 4e−x2and above the x-axis between x = 0 and x = 1 around the y-axis isV = b2𝜋rh dxa= 1 1 2𝜋x $$4e−x2  dx.0Step 3The integral 2𝜋 4xe−x2 dx can be done with the substitution u = $$−x2 and du = $$−2x dx.Step 4With the substitution, we have 2𝜋 4xe−x2 dx = − $$4π eu du = − $$4πeu + C.Step 5Going back to x, the volume of our solid is

Find the volume of the solid obtained by rotating the region bounded by x, equals, minus, 6, plus, y, squaredx=−6+y 2 and x, equals, minus, yx=−y about the line x, equals, minus, 9x=−9. Round to the nearest thousandth.

Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis.y = x3/2,    y = 8,    x = 0

How is integration used in finding the volume of a solid of revolution