The attachments below are 7 Calculus 2 quizzes they range from 15-10 questions the instructions are : Please extend sufficient space for solutions using the docx version, if you like to work on the qu

MATH 141 Calculus II Quiz 2 Write your name. Write solutions in details. Box your answers Find the volume of the solid generated by revolving this region about the x-axis. 1. 2. 3. A base of a solid is the region bounded by , the x-axis, the y-axis, and the line Each cross -section perpendicular to the x-axis is a square. Find the volume of the solid. 2, 0 3 y x x=   1142 sin , y x x  =   x ye − = 1. x= 2 4. The base of a solid is the disk bounded by the circle . Find the volume of the solid given that the cross -sections perpendicular to the x-axis are squares . For problems 5 and 6, f ind the volume of the solid generated by revolving this region about the y- axis. (Hint : draw a picture .) 5. 6. 2 2 2x y r += 3, 2, 0 y x x y= = = , 4, 0 y x x y= = = 3 7. The force of gravity exerted by the Earth on a mass m at a distance r from the center of the Earth is given by Newton’s formula, , where M is the mass of the Earth and G is the univers al gravitational constant. Fin d the work done by gravity in pulling a mass m from to . 8. Find the work done by a force F, in pounds, that moves a particle along the x-axis from feet to feet, if . 9. A cylindrical reservoir of diameter 4 feet and height 6 feet is half -full of water weighing w pounds per cubic feet. Find the work done in emptying the water over the top. 2 mM FG r =− 1 rr= 2 rr= 4 x= 9 x= 1 () 2 Fx x = 4 10. Find the area of the surface generated by revo lving the curve about the x-axis. 11. Calculate the length of the arc . 12. Find the centroid of the region bounded between the graph , x-axis, and the vertical line . ( ) 2 1 , 1 0f x x x = − −   16 ( ) 2 cos , ( ) 2 sin , 0x t t y t t t  = =   2 yx= 1 x=