Calculus
posted by Megan .
alright. i need to write a definite integral for the volume and evaluate the integral for the region bounded by y=x^2, y=0, and x=1 revolved about the a) xaxis, b) the yaxis, c) x=2, and d) y=2.
HELP!
Lets do the x=2 axis.
dV= pi rh dr where r is radius, h is height. r= x1 dr=dx h= y=x^2
dV= PI (x1)x^2 dx
Then integrate from x=1 to 2
So the idea is to draw the pic, make an incremental dV in terms of r and h, change those to x,y variables.
What about rotating about y=6
dV= PI r h dr
r= 6y y goes from 0 to 1^2
dr= dy
h= 1sqrt(y)
check that picture
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