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

Reiny
need the intersection ....
3x = 4x
4x=4
x = 1
height of revolved region = radius of rotation
= 4x  3x = 4  4x
area = ∫(44x) dx from 0 to 1
= [4x  2x^2] from 0 to 1
= (4  2)  0
= 2
volume = π∫ (44x) 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
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