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.

calculus 
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
Respond to this Question
Similar Questions

Calculus
This problem set is ridiculously hard. I know how to find the volume of a solid (integrate using the limits of integration), but these questions seem more advanced than usual. Please help and thanks in advance! 1. Find the volume of … 
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 curves. … 
calculus
Let R be the region in the first quadrant that is enclosed by the graph of y = tanx, the xaxis, and the line x = π/3 h. Find the area of R i. Find the volume of the solid formed by revolving R about the xaxis 
Calculus
The following are about an infinite region in the 1st quadrant between y=e^x and the xaxis. A) Find the area of the region B)Find the volume of the solid generated by revolving the region about the yaxis 
CALCULUS HELP PLZ
The region R is bounded by the xaxis, yaxis, 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 xaxis. C. The solid formed in part B is divided … 
CALCULUS
The region R is bounded by the xaxis, yaxis, 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 xaxis. C. The solid formed in part B is divided … 
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 solid … 
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. The region R is the base of a solid. For this solid, the cross sections, … 
Calculus
find the volume of the solid formed by revolving the region bounded by the graphs of y=x^3 y=1 x=2 about the yaxis 
Calculus
Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by y = x^3 y = 16 x about the xaxis.