Area Between Curves
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
Find the volume of the solid generated by revolving the given curves around the x-axis.
y = 9 - x2
y = 0
324π/5
Find the volume when cross sections taken perpendicular to the x axis are squares:
y = sqrt(x)
x = 3
y = 0
9/2
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
Find the area between curves:
y = 2x - x2
y = x2
1/3
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
Find the volume when cross sections taken perpendicular to the x axis are semi-circles:
x + 4y = 4
y = 0
x = 0
π/6
Find the volume of the solid generated by revolving the given curves around y axis.
y = 5x - x2
y = 0
3125π/12
Find the area between curves:
y = x2 - 2x
y = x + 4
125/6
Find the volume of the solid generated by revolving the given curves around the x axis.
y = x2
y = 3x
162π/5
Find the volume when cross sections taken perpendicular to the y axis are triangles:
y = 1 - x
x = 1 - y
sqrt(3)/12
Find the volume of the solid generated by revolving the given curves around y = -2.
x = y2 + 1
x = 2
16π/3
Find the area between curves:
y = sqrt(x + 2)
y = 1/(x + 1)
[0, 2]
16/3 - ln|3| - (4sqrt(2))/3
Find the volume of the solid generated by revolving the given curves around y = 2.
y = e-x
y = 1
x = 2
~9.526
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
Find the volume of the solid generated by revolving the given curves around x = 1.
y = 4x - x2
y = 3
8π/3
Find the area between curves:
y = cos(πx)
y = 4x2 - 1
8/3
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))
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."
Find the volume of the solid generated by revolving the given curves around x = 1.
y = x2
y = 2 - x2
16π/3