The triple integral ∫∫∫V1dV∫∫∫𝑉1𝑑𝑉 represents the volume of the region V𝑉 in 3D space.Select one:TrueFalse

For the triple integral: ∫0𝑎∫04𝑦∫0𝑔(𝑥,𝑦)𝑓(𝑥,𝑦,𝑧)𝑑𝑧𝑑𝑥𝑑𝑦what is the order at which the integral should be evaluated? Group of answer choiceswith respect to x then y then zwith respect to z then y then xwith respect to z then x then ywith respect to y then x then z

The volume of the sphere x2+y2+z2=1𝑥2+𝑦2+𝑧2=1 is evaluated by:a.4∫10∫1−y2√01−x2−y2−−−−−−−−−√dxdy4∫01∫01−𝑦21−𝑥2−𝑦2𝑑𝑥𝑑𝑦b.8∫10∫1−y2√01−x2−y2−−−−−−−−−√dxdy8∫01∫01−𝑦21−𝑥2−𝑦2𝑑𝑥𝑑𝑦c.8∫10∫101−x2−y2−−−−−−−−−√dxdy8∫01∫011−𝑥2−𝑦2𝑑𝑥𝑑𝑦d.16∫10∫1−y2√01−x2−y2−−−−−−−−−√dxdy

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.

In the region of free space that includes the volume 2 < x,y,z < 3.D = [ (2y/z)ax + (2x/z)ay - (4xy/z2)az) ] C/m2(i) Evaluate the volume integral side of the divergence theorem for the volumedefined by 2 < x,y,z < 3

Find the volume of the solid bounded by the planes x = 1, y = 0, z = 0, theparabolic cylinder y = x2, and the surface z = xey. Sketch the region of integration