C3 Volumes of revolution questions

The image is too small to read.

this may be useful:

http://answers.yahoo.com/question/index?qid=20090613050032AA4Eg73

although there are problems with the image here also...

I've just solved the question regarding the image, however like I asked the bear, I wasn't sure what is the best way of explaining that inserting infinity into [3x^1/3] gives infinity.

Would you be able to help with the second question?



Thanks, I didn't realise that through integrating it, you'd be able to show that it tends to infinity. You end up with [3x^1/3] infinity and 1

What is the best way to phrase that if you plug in infinity, then the number will get infinitely big? (Or is that okay?)

just say that the result is infinitely big

Thanks, would you be able to take a look at my working for the second question?

If you were to show that there was an asymptote on the x-axis, that would do. I personally would do this by substuting 0 for y in the equation, you shouldn't be able to do this.. I've never seen that kind of question on a C3 paper, but I'm talking about OCR so it might depend on the exam board. I might be completely wrong here.

Could you type out the equation, because I can't see it, and I'm able to help you with your working for the next question if you like.

Ah okay, I'm on OCR as well Type out the equation for what, the first or the second one? The first one is :y=x^-2/3 the second is included in the question. I followed that link to yahoo answers, and it said that you integrate it, then set the limits as infinity and 1, and that shows that it tends to infinity.

If you could help with the next question, it would be great.

Oh ok, so because you're doing OCR, I wouldn't worry about the first question, it won't come up on the exam.

b) so you'd do the integral limits 0 and 1 takeaway the area of the white square $\int^1_0 x^{-\frac{2}{3}} dx - 1$

have you done that?

Oh ok, so because you're doing OCR, I wouldn't worry about the first question, it won't come up on the exam.

b) so you'd do the integral limits 0 and 1 takeaway the area of the white square $\int^1_0 x^{-\frac{2}{3}} dx - 1$

have you done that?

Hi again, I'm a little bit confused. Under the "Who quoted me" it says that you quoted me in this thread 15 minutes ago, but I was the last poster?

Er I think we're talking about 2 different questions Are you talking about this one? :
2. The part of the graph between y=e^0.5x, the line y=2 and the y axis is rotated about the x-axis to make a solid of revolution. Find the volume of this solid, giving your answer in the form pi(aln(b) - c)

Oh lol, I was looking at 1b hehe
I'll have to get a pen out

ok, so here's my working out. First I worked out where the line y = 2 and the curve meet, to find the limits.
$[br]2 = e^{\frac{1}{2}x}[br]\dfrac{1}{2}x = ln2[br]x = ln4[br][br]\pi (\int^{ln2}_0 4 dx - \int^{ln2}_0 (e^{\frac{1}{2}x})^2)[br]\int^2_0 \pi (e^x) dx[br]\pi (\left[ 4x \right]^{ln2}_0 - \left[ e^x \right]^{ln2}_0[br]\pi ((4ln4 - 0) - (e^{ln4} - 1))[br]\pi (4ln4 - 4 - 1)[br]\pi (4ln4 - 5)[br]$
that took too long to type out...

I have a few questions, firstly, you found that x = ln4. Should the limits for the integral be ln4 then? And why are you doing the integral of e^0.5x and then subtracting y=2? Isn't y=2 just a boundary? (It's probably unclear what I'm saying, but you have [4x] and [e^x] however I don't see why you used two integrals?)

Also, the answer is pi(8ln2 - 3)

oh no, ok let me have another look through

Okay thanks How's your revision going, have you started papers yet?

I have a few questions, firstly, you found that x = ln4. Should the limits for the integral be ln4 then? And why are you doing the integral of e^0.5x and then subtracting y=2? Isn't y=2 just a boundary? (It's probably unclear what I'm saying, but you have [4x] and [e^x] however I don't see why you used two integrals?)

Also, the answer is pi(8ln2 - 3)

of course I've started papers lol! of course, that is the best revision for maths C3.

I have all of the papers except the 2011 and 2012 ones and solutions on fronter, so I've been working my way back from 2010. I've been focusing on my other subjects though, they're sooner.

Y = 2 is a horizontal line, so you have to find the volume that makes and takeaway the volume y = e^0.5x makes

Y = 2 is a horizontal line, so you have to find the volume that makes and takeaway the volume y = e^0.5x makes