Calculus Chap. 6 Review

Area Between Curves

100

If both curves are in terms of simple form f(y) = , will the area of the region be in terms of x or y?

y

200

Find the area between curves:

y = 2x - x²

y = x²

1/3

300

Find the area between curves:

y = x² - 2x

y = x + 4

125/6

400

Find the area between curves:

y = sqrt(x + 2)

y = 1/(x + 1)

[0, 2]

16/3 - ln|3| - (4sqrt(2))/3

500

Find the area between curves:

y = cos(πx)

y = 4x² - 1

8/3

Disks and Washers

100

Find the volume of the solid generated by revolving the given curves around the x-axis.

y = 9 - x²

y = 0

324π/5

200

Find the volume of the solid generated by revolving the given curves around the x-axis.

y = cos(x)

y = 0

x > π/4

~0.4483

300

Find the volume of the solid generated by revolving the given curves around the x axis.

y = x²

y = 3x

162π/5

400

Find the volume of the solid generated by revolving the given curves around y = 2.

y = e^-x

y = 1

x = 2

~9.526

500

Find the volume of the solid generated by revolving the given curves around y = 1.

y = 1 + sec(x)

y = 3

2π(4/3π - sqrt(3))

V of Solids w/Cross-Section

100

Find the volume when cross sections taken perpendicular to the x axis are squares:

y = sqrt(x)

x = 3

y = 0

9/2

200

Find the volume when cross sections taken perpendicular to the x axis are semi-circles:

x + 4y = 4

y = 0

x = 0

π/6

300

Find the volume when cross sections taken perpendicular to the y axis are triangles:

y = 1 - x

x = 1 - y

sqrt(3)/12

400

Find the volume when cross sections taken perpendicular to the x axis are right isosceles triangles w/hypotenuse in the base:

y = 5x - x²

y = 0

~54.308333

500

What is 0/0?

"Imagine that you have zero cookies and you split them evenly among zero friends. How many cookies does each person get? See? It doesn't make sense. And Cookie Monster is sad that there are no cookies, and you are sad that you have no friends."

Shells

100

Find the volume of the solid generated by revolving the given curves around the y = 1.

y = x³

x = 0.9

y = 0

5π/14

200

Find the volume of the solid generated by revolving the given curves around y axis.

y = 5x - x²

y = 0

3125π/12

300

Find the volume of the solid generated by revolving the given curves around y = -2.

x = y² + 1

x = 2

16π/3

400

Find the volume of the solid generated by revolving the given curves around x = 1.

y = 4x - x²

y = 3

8π/3

500

Find the volume of the solid generated by revolving the given curves around x = 1.

y = x²

y = 2 - x²

16π/3