# 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 divided into two solids of equal volume by a plane perpendicular to the
x-axis. Find the x-value where this plane intersects the x-axis.

1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩
1. A.
∫[0,3] 1/√(x+1) dx
= 2√(x+1) [0,3]
= 2

B. using discs, v=∫πy^2 dx
= π∫[0,3] 1/(x+1) dx
= πlog(x+1) [0,3]
= πlog4

C. We want c where
π∫[0,c] 1/(x+1) dx = π∫[c,3] 1/(x+1) dx
log(c+1)-log(0+1) = log(3+1)-log(c+1)
2log(c+1) = log(4)
log(c+1) = log(2) (and not because 4/2=2)
c = 1

1. 👍
2. 👎
3. ℹ️
4. 🚩

## Similar Questions

1. ### Calculus

A base of a solid is the region bounded by y=e^-x, the x axis, the y axis, and the line x=2. Each cross section perpendicular to the x-axis is a square Find the volume of the solid

2. ### calculus

let R be the region bounded by the x-axis, the graph of y=sqrt(x+1), and the line x=3. Find the area of the region R

3. ### 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

4. ### mathematics

find the volume of the solid of revolution generated when the region bounded by the curve y =x^2,the x-axis, and the lines x = 1 and x = 2 is revolved about the x-axis.

1. ### Calculus

1. Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line x = 6. y = x, y = 0, y = 5, x = 6 2. Use the method of cylindrical shells to find the volume V generated by

2. ### Calculus 2

The region bounded by the given curves is rotated about the specified axis. Find the volume of the resulting solid by any method. y2 − x2 = 4, y = 3; about the x-axis

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 base of a solid is the region in the first quadrant bounded by the graph of y = 3/(e^x) , the x-axis, the y-axis, and the line x=2. Each cross section of this solid perpendicular to the x-axis is a square. What is the volume

1. ### calculus

1. Find the volume V obtained by rotating the region bounded by the curves about the given axis. y = sin(x), y = 0, π/2 ≤ x ≤ π; about the x−axis 2. Find the volume V obtained by rotating the region bounded by the curves

2. ### 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? b. Find the volume of the solid generated when region R is rotated about the x axis. c. Find all

3. ### calculus

Find the volume of the solid generated by revolving the region about the given line. The region in the second quadrant bounded above by the curve y = 16 - x2, below by the x-axis, and on the right by the y-axis, about the line x =

4. ### AP Calculus

Let R be the region bounded by the x-axis and the graph of y=6x-x^2 Find the volume of the solid generated when R is revolved around the y-axis