CAS Calc Jeopardy!!

Washer/Disk

100

Find the volume if the region enclosing y=x-1, y=0, and x=3 is rotated about the x-axis. 

4pi

300

Find the volume if the region enclosing y=2x, y=0, and x=3 is rotated about the line y=6. 

72pi

500

Find the volume if the region enclosing y=1+sqrt(x), y=1, and x=4 is rotated about the line y=5.

~52.00pi

Surface Area

100

Find the surface area of the curve generated by revolving the given curve about the x-axis. 

8pi

300

Find the surface area generated by revolving the given curve about the y-axis:

x=sqrt(9-y^2), -2<y<2.

24pi

500

Find the surface area generated by revolving the curve about the stated axis.

y=sqrt(x) + (1/3)x^(3/2), 1<x<3 ; x-axis

16pi/9

Shell

100

Find the volume if the region enclosing y=2x, y=0, and x=3 is rotated about the y-axis.

36pi

300

Find the volume if the region enclosing y=x^2, y=0, and x=4 is rotated about the line x=4.

128pi/3

500

Find the volume of the solid generated when the region enclosed by the given curves is revolved about the y-axis. 

y=(1/(x^2+1)), x=0, x=1, and y=0.

pi(ln2)

Integration!

100

Integrate the term:

x(1-sqrt(x))

1/2x^2 - 2/5x^5/2 + c

300

Evaluate the antiderivative of (1-x)e^-x with boundaries of infinity and 0.

Converges to 0

500

Evaluate the antiderivative of (4x-4)/(x^2-4)

ln(x-2) + 3ln(x+2) + c

Area Under a Curve

100

Calculate the area enclosed by the curve y=4x-x^2 and the line y=3.

4/3

300

Calculate the area between y = x^2 - 4x + 8 and y = 8 + 4x - x^2.

64/3

500

Calculate the area between the curves -sqrt(x) and 2sqrt(x), with x boundaries x=0 and x=4.

16.00