Find volume when curve rotated about y-axis

[DeusAbscondus]

Hi folks, could someone please take a look at this for me:

Here are the givens:

$$\text{ Find the volume when this curve is rotated about the y-axis }$$
$$y=-4lnx\ \text{ where } 0\le y \le 2$$

I have set my working out in a geogebra file, taken a screenshot and attached same below.

Would someone kindly take a look at my calculations and point out where I am going astray?

Really appreciate your time,
Deus Abs

 

[tkhunny]

$$e^{0}\ne 0$$

Good work otherwise.

 

[DeusAbscondus]

$$e^{0}\ne 0$$

Good work otherwise.

Thank you kindly!

so: $$-2.2114547+2\pi \approx 3.97$$

Which is the solution given!

Do you know I kept making that error over and over again, through a frustrating hour or so; this makes me *sure* that I must find a different approach (different mind-set/attitude, perhaps) my checking procedure: cultivate an attitude of radical skepticism: something like: "question *everything* again regarding your working assumptions!"

Regs,
D'Abs

 

[tkhunny]

Contrary to the too broad definition of privacy, another pair of eyes often is quite beneficial. :)

 

[MarkFL]

Very true! Oftentimes when I make an error like that, I will keep blindly making it over and over, and the best thing for me is to move on to something else, and when I come back to it after a break, then I am much more likely to catch the error. If I don't, then I will seek another pair of eyes! ;)