PROBLEM 1: Select one from the following applications regarding volume of a solid of revolution. You will be expected to provide a complete solution of the problem including a graph of the shaded region, a sketch of the solid and typical element, the integral, the antiderivative, and the calculation of the answer. Also, state whether you are using disks, washers, or shells.
Determine the volume of the solid generated by revolving the region enclosed by the curves given.
a. y=1+x^(3),x=1,x=2, and y=0 about the x-axis.
b. ,y=x^(2)+1,y=x+3 about the x-axis.
c. y=x^(3),x=0,y=1 about the y-axis.
d. y=(2)/(x),y=1,y=3,x=0 about the y-axis.
e. y=sqrt(x),x=4,x=9,y=0 about the y-axis.
f. ,y=2x-x^(2),y=0 about the y-axis.
g. x=2,y=2,y=3,x=0 about the x-axis
h. y=x^(2),x=1,y=0 about the x-axis
PROBLEM 1: Select one from the following applications regarding volume of a solid of revolution. You will be expected to provide a complete solution of the problem including a graph of the shaded region, a sketch of the solid and typical element, the integral, the antiderivative, and the calculation of the answer. Also, state whether you are using disks, washers, or shells.
Determine the volume of the solid generated by revolving the region enclosed by the curves given. a. y =1 + x3, x =1, x = 2,and y = 0 about the x-axis. b. y = x2 + 1, y = x +3about the x-axis. C. y=x3, x = 0, y=1 about the y-axis. d. e. y = Vx, x = 4, x =9, y = 0 about the y-axis. f. y = 2x - x2, y = 0 about the y-axis. g. x = 2,y =2,y =3,x = 0 about the x-axis h. y = x2,x =1,y = 0 about the x-axis