Saturday

April 19, 2014

April 19, 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

**Related Questions**

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

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

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

Calculus - Let R be the region in the first quadrant under the graph of y=1/sqrt...

calculus - Find the volume of the solid generated by revolving the region about ...

Calculus - Find the volume of the solid generated by revolving the following ...

calculus - The figure shows the region bounded by the x-axis and the graph of . ...

calculus - let R be the region bounded by the x-axis, the graph of y=sqrt(x+1), ...

calculus - Sketch the region enclosed by x+y^2=42 and x+y=0. Decide whether to ...

Physics - The wavelength of the electromagnetic waves is 200 nm. Which of ...