Tuesday

September 16, 2014

September 16, 2014

Posted by **Taeyeon** on Friday, March 9, 2012 at 12:43pm.

a. Find the area of region R.

b. Find the volume of the solid formed by revolving the region R about the x-axis.

- calculus -
**Reiny**, Friday, March 9, 2012 at 1:06pmneed 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

**Answer this Question**

**Related Questions**

calculus - 1. Let S be the region in the first quadrant bounded by the graphs of...

calculus - Sketch the region in the first quadrant enclosed by the given curves...

calculus - Let R be the region in the first quadrant that is enclosed by the ...

calculus - Which has more area, the region in the first quadrant enclosed by the...

Calculus - The region in the first quadrant enclosed by the graphs of y = x and ...

Calculus 1 - Let f be the function given by f(x)=3sqrt(x-2). A) On the axes ...

calculus - Consider the graphs of y = 3x + c and y^2 = 6x, where c is a real ...

calculus - 2. Sketch the region in the first quadrant that is bounded by the ...

Calculus - The following are about an infinite region in the 1st quadrant ...

calculus - Let R be the region in the first quadrant bounded by the graphs of y=...