Area by washers and/or cylindrical shells: other than x,y

  • Thread starter tsamocki
  • Start date
  • #1
20
0
What if you want to rotate around something other than the x/y axis?

For example:

Homework Statement



y=x, y=0, x=1, rotated around the line x=-1

Homework Equations



NumberedEquation1.gif


or

NumberedEquation1.gif


The Attempt at a Solution



V= ⌠(between 0 and 1)π[1+x]^2 dx

= π(1/3(x)^3+x^2+2x),x=0, x=1

=π((1/3)(1)^3+(1)^2+2(1))-0

= 10π/3

Shell method:

V= ⌠(between 0 and 1)2πx(x+1)dx

=2π((1/2)x^2+(1/3)x^3)x=1,x=0

=2π((1/2)+(1/3))-0

=2π(5/6)

=5π/3

Obviously the two answers do not match (i don't even know if i am correct on either); where am i going wrong?

Thanks in advance!
 

Answers and Replies

  • #2
324
0
unless im mistaken, if you're using the first equation you have to do it with respect to y...

and when you did it the second way, the expression inside of the integral is wrong.
 

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