# calculus

1. Let R be the region in the first quadrant enclosed by the graphs of y=4-X , y=3x , and the y-axis.
a. Find the area of region R.
b. Find the volume of the solid formed by revolving the region R about the x-axis.

1. 0
2. 0
3. 27
1. need the intersection ....
3x = 4-x
4x=4
x = 1
height of revolved region = radius of rotation
= 4-x - 3x = 4 - 4x

area = ∫(4-4x) dx from 0 to 1
= [4x - 2x^2] from 0 to 1
= (4 - 2) - 0
= 2

volume = π∫ (4-4x) dx from 0 to 1
= π∫(16 - 32x + 16x^2) dx from 0 to 1
= π[16x - 16x^2 + (16/3)x^3 ] from 0 to 1
= π( 16 - 16 + 16/3 - 0)
= 16π/3

check my arithmetic

1. 0
2. 0
posted by Reiny

## Similar Questions

1. ### Calculus

The region in the first quadrant enclosed by the graphs of y = x and y = 2sin(x) is revolved about the x-axis. The volume of this solid is: (a) 1.895 (b) 2.216 (c) 5.811 (d) 6.678 (e) 13.355

2. ### calculus

Which has more area, the region in the first quadrant enclosed by the line x+y=1 and the circle x^2+y^2=1, or the region in the first quadrant enclosed by the line x+y=1 and the curve sqrt(x)+sqrt(y)=1? Justify your answer.

asked by Sophie on January 21, 2010
3. ### calculus

Consider the graphs of y = 3x + c and y^2 = 6x, where c is a real constant. a. Determine all values of c for which the graphs intersect in two distinct points. b. suppose c = -3/2. Find the area of the region enclosed by the two

asked by mary on March 24, 2010
4. ### Calculus

Let f and g be the functions given by f(x)=1+sin(2x) and g(x)=e^(x/2). Let R be the shaded region in the first quadrant enclosed by the graphs of f and g. A. Find the the area of R. B. Find the value of z so that x=z cuts the

asked by Anonymous on April 19, 2015
5. ### Calculus

Let R be the first quadrant region enclosed by y=e^2, y=e^x and the y-axis. The area of region R is? I don't understand why is the interval is from [0-2]. Thanks

asked by Mike on March 12, 2017
6. ### Calculus 2

Sketch the region in the first quadrant enclosed by y=7/x, y=2x, and y=x/2. Decide whether to integrate with respect to x or y. Then find the area of the region.

asked by Henry on February 9, 2016
7. ### calculus

Sketch the region in the first quadrant enclosed by y=6/x, y=2x, and y=12x. Decide whether to integrate with respect to x or y. Then find the area of the region.

asked by Nick on July 18, 2015
8. ### calculus

R is the first quadrant region enclosed by the x-axis, the curve y = 2x + a, and the line x = a, where a > 0. Find the value of a so that the area of the region R is 18 square units.

asked by Bree on May 20, 2016
9. ### calculus

R is the first quadrant region enclosed by the x-axis, the curve y = 2x + b, and the line x = b, where b > 0. Find the value of b so that the area of the region R is 288 square units.

asked by Anonymous on August 29, 2015
10. ### calculus

Let A be the bounded region enclosed by the graphs of f(x) = x , g(x) = x3 . Find the volume of the solid obtained by rotating the region A about the line x + 2 = 0.

asked by me on October 31, 2010

More Similar Questions