Calc 2
posted by Melissa .
Find the area of the surface generated when y=4x and x=1 is revolved about the yaxis.

No calculus need for this one. It's just a cylinder with a cone cut out.
r=1
h=4
v = πr^2h  π/3 r^2h = 2π/3 r^2h = 8π/3
Ok ok. If you want to use calculus, then with shells,
v = ∫[0,1] 2πrh dx
where r=x and h=y=4x
v = ∫[0,1] 2πx*4x dx = 8π/3
using discs (washers) you get
v = ∫[0,4] π(R^2r^2) dy
where R=1 and r=x=y/4
∫[0,4] π(1y^2/16) dy = 8π/3 
We have to use the Surface area of revolution formula
integral(f(x) aqrt(1+f'(x)^2))
Respond to this Question
Similar Questions

calculus
find the volume generated by the boundaries y=x^3+1 , xaxis , x=1 , x=2 revolved about yaxis 
Calc
Set up and evaluate the definite integral for the area of the surface generated by revolving the curve about the xaxis. y = (x³/6) + (1/2x), 1≤ x ≤ 2 
Calc
Set up and evaluate the definite integral for the area of the surface generated by revolving the curve about the yaxis. y = cube rt. (x) + 2 Thank you so much!! 
Calculus (Solid of Revolution)
The region R is bounded by the xaxis, x = 1, x = 3, and y = 1/x^3. C. Find the volume of the solid generated when R is revolved about the xaxis. 
calc
1. Let R be the region bounded by the xaxis, the graph of y=sqr(x) , and the line x=4 . a. Find the area of the region R. b. Find the value of h such that the vertical line x = h divides the region R into two regions of equal area. … 
calculus 2
The curve y=sinh(x),0<=x<=1, is revolved about the xaxis. Find the area of the resulting surface. 
CALCULUS problem
There are four parts to this one question, and would really appreciate if you could show and explain how you get to the answer, because I tried looking up how to find the answer myself, but nothing made sense. Thank you! 11. The region … 
calculus1
Region R is bounded by x=22y^2 and x=1y^2 find the volume of the solid generated if R is revolved about the yaxis Anybody help me with this? 
Calc 2 Urgent Surface Area
Find the area of the surface generated when y=4x and x=1 is revolved about the yaxis. We have to use the surface area formula. 
Calc 2 Urgent Surface Area of Revolution Question
Find the area of the surface generated when y=4x and x=1 is revolved about the yaxis. We have to use the surface area formula of revolution. Integral (2pi*f(x)sqrt(1+f'(x)^2))dx