Question

Use a Maple utility to compute and calculate the following:

Find the volume of the solid generated by revolving the region bounded by y=1-x^3, y=1, and x=-2 about the line y=10

a.) Using the disc method.

b. Using the shell method.

Problem 2

Find the arc length of the semicircle y=sqrt(4-x^2) from (-sqrt(3),1) clockwise to (sqrt(3),1).

problem 3

Find the area of the surface of revolution generated by revolving the plane curve y=3x^(1/3) over [1,8] about the y-axis.

problem 4

A force of 6 pounds is needed to stretch a 14-inch spring 3 inches. Find the work done in additional stretching the spring to the length of 20 inches?

problem 5

Find the moments Mx and My about the x-axes and y-axes, and the center of mass for the lamina of uniform density bounded by y=4-x^2 and y=0.

Answer 1

1 Solution Give that Stvetch yinch Spring = 3inch. engt20 inche we know that 12- fL 2 3 inch -3-ft 1 2 hiven forca tis 6 ls Stret ching Spving 2. 14 -3 12 2 4 -3 2. 1 2

→ k: 6x12. then force to Stretching Spvin Up to 20ioch inches- 20 ft 2 Work doeW - 2 0 12. 2.0 36 20 1 2 3 6 - ftlb

Note!- As per the Cheg utdeline ave allowed to Solve Only I uestion. So, please γepost the remain- ues tions. Thank you