https://imgur.com/gallery/lODhz

Find the volume of the solid generated by rotating the region about the y axis. I get 2 Pi u^3 but the solution is Pi/2 u^3

https://imgur.com/gallery/lODhz

Find the volume of the solid generated by rotating the region about the y axis. I get 2 Pi u^3 but the solution is Pi/2 u^3
What was the integral you obtained when trying to calculate the volume?

Originally Posted by InteGrand
What was the integral you obtained when trying to calculate the volume?
This is what I got.

https://imgur.com/gallery/Zvbc3

You have the correct integral and correct antiderivative. You have just made an error in evaluating

$\left[\frac{y^2}{2} -3y\right]_{3}^{4}.$

So you can have another go at evaluating this (carefully). Make sure to get all signs right when evaluating it (you have a sign error in your fourth-from-last line).

$\noindent By the way, by either using a substitution or considering a translation of a graph, we have$

$\int_{3}^{4}(y-3)\, dy = \int_{0}^{1}y \, dy,$

$\noindent and you should find this latter integral is easier to calculate.$

Thanks I'm such an idiot silly mistake

Originally Posted by InteGrand
You have the correct integral and correct antiderivative. You have just made an error in evaluating

$\left[\frac{y^2}{2} -3y\right]_{3}^{4}.$

So you can have another go at evaluating this (carefully). Make sure to get all signs right when evaluating it (you have a sign error in your fourth-from-last line).
Can you please check where I'm making a mistake for this question below.

https://imgur.com/gallery/elmgK

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