# Calculus

posted by .

The region bounded by y=-x^2+14-45 and y=0 is rotated about the y-axis, find the volume.

• Calculus -

The region goes from x=5 to x=9, So,

using shells,

v = ∫[5,9] 2πrh dx
where r = x and h=y
v = 2π∫[5,9] x(-x^2+14x-45) dx
= 448/3 π

Using discs (washers), things get a bit more complicated, because there are two branches to the parabola.

y = 4-(x-7)^2
x = 7±√(4-y)

v = ∫[0,4] π(R^2-r^2) dy
where R = 7+√(4-y) and r = 7-√(4-y)
v = π∫[0,4] (7+√(4-y))^2 - (7-√(4-y))^2) dy
= 448/3 π

## Similar Questions

1. ### Calculus

find the volume of the region bounded by y=e^x, y=0, x=-1, x=1 rotated about the x axis
2. ### Calc

The region bounded by y=2.5x^2 and y=4x is to be rotated about both axes and the volume generated calculated by both the washer and the shell methods. 1)The volume of the region bounded by y=2.5x^2 and y=4x, when rotated about the …
3. ### Calculus

Let R be the region bounded by y=6sin((pi/2)x), y=6(x-2)^2, y=3x+3 containing the point (2,6). Find the area of R, find the volume of R rotated about the x-axis, find the volume of R rotated about the y-axis, and Suppose R is the base …
4. ### Calculus Help!!

Region R is bounded by the functions f(x) = 2(x-4) + pi, g(x) = cos^-1(x/2 - 3), and the x axis. a. What is the area of the region R?
5. ### Calculus

1. Find the area of the region bounded by the curves and lines y=e^x sin e^x, x=0, y=0, and the curve's first positive intersection with the x-axis. 2. The area under the curve of y=1/x from x=a to x=5 is approximately 0.916 where …
6. ### Calculus

We're learning disks, shells, and cylinders in school but we have a substitute and I've been trying to teach this to myself. Can you check them please?
7. ### Calculus

We're learning disks, shells, and cylinders in school but we have a substitute and I've been trying to teach this to myself. Can you check them please?
8. ### Calculus

The region bounded by y= e^x, y=0, x= -1 and x=1 is rotated about the x-axis, find the volume generated.
9. ### Calculus

The region bounded by y= e^x, y=0, x= -1 and x=1 is rotated about the x-axis, find the volume generated.
10. ### calculus

The region bounded by the given curves is rotated about the specified axis. Find the volume V of the resulting solid by any method. y = −x2 + 7x − 12, y = 0; about the x-axis

More Similar Questions