# Calculus

Find the volume of the solid formed by rotating the region bounded by the graph of y equals 1 plus the square root of x, the y-axis, and the line y = 3 about the line y = 5.

1. 👍
2. 👎
3. 👁
1. draw the region. Using discs (washers), the volume is

v = ∫[0,4] π(R^2-r^2) dx
where R = 5-y and r = 5-3=2
v = ∫[0,4] π((5-(1+√x))^2-(2)^2) dx = 40π/3

1. 👍
2. 👎
2. using cylinders, we have

v = ∫[1,3] 2πrh dy
where r=5-y and h=x=(y-1)^2
∫[1,3] 2π(5-y)(y-1)^2 dy = 40π/3

1. 👍
2. 👎
3. Thank you steve.

1. 👍
2. 👎

## Similar Questions

1. ### Calculus

Find the volume of the solid obtained by rotating the region bounded by y= x^(1/3), and y= x about the line y=1

2. ### calculus

Consider the solid obtained by rotating the region bounded by the given curves about the x-axis. y = 9 - 9x^2 , y = 0 Find the volume V of this solid. Sketch the region, the solid, and a typical disk or washer. Any help or tips

1) Find the area of the region bounded by the curves y=arcsin (x/4), y = 0, and x = 4 obtained by integrating with respect to y. Your work must include the definite integral and the antiderivative. 2)Set up, but do not evaluate,

4. ### Calculus

Find the volume of the solid obtained by rotating the region bounded by y= x^2, y=0, and x=3 about the x-axis.

1. ### Calculus

Find the volume of the solid obtained by rotating the region bounded by the curves y=cos(x), y=0, x=0, and x=π/2 about the line y=1.

2. ### calculus

Find the volume of the solid obtained by rotating the region bounded by y=x and y=√x about the line x=2. Volume =

3. ### Calculus

a) Find the volume formed by rotating the region enclosed by x = 6y and y^3 = x with y greater than, equal to 0 about the y-axis. b) Find the volume of the solid obtained by rotating the region bounded by y = 4x^2, x = 1, and y =

4. ### CALCULUS

The region R is bounded by the x-axis, y-axis, x = 3 and y = 1/(sqrt(x+1)) A. Find the area of region R. B. Find the volume of the solid formed when the region R is revolved about the x-axis. C. The solid formed in part B is

1. ### K

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 3e^(-x), y = 3, x = 2; about y = 6

2. ### cal

Find the volume of the solid obtained by rotating the region bounded by y=4x^2,x=1,y=0 about the x-axis.

3. ### Calculus

Let f be the function given by f(x)=(x^3)/4 - (x^2)/3 - x/2 + 3cosx. Let R be the shaded region in the second quadrant bounded by the graph of f, and let S be the shaded region bounded by the graph of f and line l, the line

4. ### calculus

1. Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = ln(5x), y = 1, y = 3, x = 0; about the y-axis 2. Use the method of cylindrical shells to find the volume V