Revolving Solids

[carolinepicard29]

2 Questions

1. A parabola P is symmetric to the y-axis and passes through (0,0) and (b, e^{-b^2}) where b > 0.
(a) Write an equation for P.
(b) The closed region bounded by P and the line y= e^{-b^2} is revolved about the y-axis to form a solid figure F. Compute the volume of F.
(c) For what value of b is the volume of F a maximum? Justify your answer.

What I have so far is that P will be y=ax² where e^{-b^2}= a(b²⁾
but I'm not sure how to solve that.

2. Line L is tangent to y = ln x at point P and passes through the point (0, 0). Region R is bounded by the graphs of y = ln x,
line L and the x-axis.
a) Find the equation of line L.
b) Find the area of region R.
c) Find the volume of the solid generated by revolving
region R about the line y = -1.


What I have for this one is line L is y=mx where m=derivative of y=lnx at point P. Therefore m is 1/(x coordinate of P) but I'm don't know how you're supposed to find that.
(b) is just the area between the two curves (the integral of one minus the other but I need to know the equation of L first)

 

[tkhunny]

Not sure how to solve what? You have \(\displaystyle a = \frac{1}{b^{2}\cdot e^{b^2}}\)

Were you looking for something else?