solids of revolution

What is the volume of the solid of revolution generated by rotating about the x - axis the plane region bounded by y = x and y = x 2 ? => 7 π 5 or 3 π 1 0 or 3 π 6 or 3 1 0..

Find the volume of the solid of revolution formed by revolving the region bounded by f ( x ) = 1 + 4 x and the x -axis (2 ≤ x ≤ 4) about y -axis. [Use shell method.] => 28 π or 48 π or 56 π or 68 π or 14 π..

Find the volume of the solid of revolution formed by revolving the region bounded by f ( y ) = y and the y -axis (0 ≤ y ≤ 2) about x -axis. [Use shell method.] => 1 6 π 5 cubic units or 1 6 2 π 5 cubic units or 8 2 π 5 cubic units or 3 2 π 5 cubic units or 8 &p..

Find the volume of the solid of revolution formed by revolving the region bounded by f ( y ) = y - y 2 and the y -axis (0 ≤ y ≤ 1) about x -axis. [Use shell method.] => π 6 cubic units or 7 π 1 2 cubic units or π 1 2 cubic units or π 3 cubic units or 1 4 π 1..

Find the volume of the solid of revolution formed by revolving the region bounded by f ( x ) = ln x , x -axis, x = 1 and x = e about y -axis. [Use shell method.] => 2 π ( e 2 - 1) cubic units or π ( e 2 - 1) cubic units or 2 π ( e 2 + 1) cubic units or π 2 ( e 2 + 1 ..

Differentiation deals with the rate of change while integration deals with the total change. The definite integrals are evaluated in problems relating to plane, areas, areas and volumes of solid of revolution etc. In this chapter, we confine ourselves to properties of de..

Fossil fuels, like, coal, lignite, petroleum and natural gas are non renewable natural resources. Both have an organic origin and are called hydrocarbon fuels. Coal was formed in nature as a solid from the remains of the trees buried deep inside the earth, some 500 million years ago. ..