Help please

Seed5813

New member
Joined
Jan 29, 2018
Messages
24
Ok so from y=e^(-x^2) to x=b is being revolved around the y axis and the resulting solid is 3/2 cubic units.

I set up the shell method:

2pi int_0^b (x(e^(-x^2)))dx = 3/2

u=-x^2
du=-2xdx
u at b = -b^3
u at 0 = 0

-pi int_0^(-b^2) (e^u) du = 3/2
-pi [e^(-b^2) - 1] = 3/2
e^(-b^2) - 1 = (-3/2pi)
e^(-b^2) = 1 - (3/2pi)

The right hand term is a negative number so I can't take the natural log of it, so I'm stuck. I can't find my mistake.

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Ok so from y=e^(-x^2) to x=b is being revolved around the y axis and the resulting solid is 3/2 cubic units.

I set up the shell method:

2pi int_0^b (x(e^(-x^2)))dx = 3/2

u=-x^2
du=-2xdx
u at b = -b^3
u at 0 = 0

-pi int_0^(-b^2) (e^u) du = 3/2
-pi [e^(-b^2) - 1] = 3/2
e^(-b^2) - 1 = (-3/2pi)
e^(-b^2) = 1 - (3/2pi)

The right hand term is a negative number so I can't take the natural log of it, so I'm stuck. I can't find my mistake.

No, the right side is not negative!

Maybe it's your lack of parentheses. You clearly intended -3/(2pi), having divided 3/2 by -pi, but you may have evaluated it as (-3/2)pi.

I get 1 - 3/(2pi) = 1 - 0.477465 = 0.522535
 
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