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# Integration help? watch

1. (Original post by Swayum)
Exactly. Does it all make sense?
Yes is does! Thank you so much! My will to continue was flagging serverely before I posted the question, but now I understand it it doesn't seem so scary! And thank you for showing sketching graphs of rational fuctions!

Ah, disabled rep, dang nabbit

Right... time to have a stab at the second part

(Original post by Farhan.Hanif93)
It would be easier to integrate between those limits and the answer would drop out immediately i.e. you won't need to consider the rectangle below the region explicitly as adjusting the integral like that does this.
So carry out:

But won't the -1/4 cancel out? I might just be being very dim here
2. (Original post by Jing_jing)
But won't the -1/4 cancel out? I might just be being very dim here
What he's implictly saying there is that if you shift the graph down by 1/4, you don't run into the problem of subtracting the rectangle (look at the sketch with the graph translated down by 1/4) - that's why that integral will work. Constants "cancel out" if they're somehow appearing in the bit where you plug limits in, rather than the bit where you're anti-differentiating. Don't think that makes it any easier really, but I suppose it's slightly faster.
3. (Original post by Swayum)
What he's implictly saying there is that if you shift the graph down by 1/4, you don't run into the problem of subtracting the rectangle (look at the sketch with the graph translated down by 1/4) - that's why that integral will work. Don't think that makes it any easier really, but I suppose it's slightly faster.
Oh right
I guess it's always good to have two methods, with my penchant for making silly mistakes checking using another method is always a good idea!
4. (Original post by soutioirsim)
Sorry guys, but does the graph look like this..?

Im just curious.

Yes it does
You got it much much much faster than me
5. For the second part am I going to have to use 'volumes of revolution' in C3? Because we're nowhere near that chapter yet. Worth going through the chapter myself and finishing off the question, or should I just leave it and tell her we've not covered the method yet?
6. (Original post by Jing_jing)
For the second part am I going to have to use 'volumes of revolution' in C3? Because we're nowhere near that chapter yet. Worth going through the chapter myself and finishing off the question, or should I just leave it and tell her we've not covered the method yet?
Yes but it's a very simple concept.
If you have a function f(x) and you're rotating is by 2pi around the x-axis between x=a and x=b (where b>a), then the volume of the solid formed by this is given by:

So in this case, , so substitute this in to the above expression and square it out and evaluate the resulting integral.
I'm a bit confused here though because you're telling me that you've not covered C3 properly yet but you're attempting a question that requires knowledge of partial fractions, which seems to come up in C4 in most syllabuses...
7. (Original post by Jing_jing)
For the second part am I going to have to use 'volumes of revolution' in C3? Because we're nowhere near that chapter yet. Worth going through the chapter myself and finishing off the question, or should I just leave it and tell her we've not covered the method yet?

I don't think learning the volumes of revolution stuff will do much harm, and I'm sure you won't find it difficult. For a revolution around the x-axis, the 'formula' is:

, where b = 5 and a = 4 in this case. Also, don't forget to take away the volume of the rotated rectangle (which is a cylinder).

EDIT: Farhan beat me to it
8. (Original post by Farhan.Hanif93)
Yes but it's a very simple concept.
If you have a function f(x) and you're rotating is by 2pi around the x-axis between x=a and x=b (where b>a), then the volume of the solid formed by this is given by:

So in this case, , so substitute this in to the above expression and square it out and evaluate the resulting integral.
I'm a bit confused here though because you're telling me that you've not covered C3 properly yet but you're attempting a question that requires knowledge of partial fractions, which seems to come up in C4 in most syllabuses...
(Original post by Goldfishy)

I don't think learning the volumes of revolution stuff will do much harm, and I'm sure you won't find it difficult. For a revolution around the x-axis, the 'formula' is:

, where b = 5 and a = 4 in this case. Also, don't forget to take away the volume of the rotated rectangle (which is a cylinder).\pi
Oh oops, sorry, I forgot to mention the question was FP2, not C4. I think that only the graph sketching bit was FP2 material though, pity we hadn't actually covered that yet

*waves at Goldfishy* Yep, it doesn't seem too bad! I might as well be ahead when we finally do cover it though!

It's actually a bit worrying when questions require information from C3/C4 because my teacher for further maths really wants me to do FP2 in January, and I doubt we'll have even finished C3 by then, let alone even started C4. Oh well, private study it is the

I ended up with which I think is right
9. (Original post by Jing_jing)
I think that only the graph sketching bit was FP2 material though, pity we hadn't actually covered that yet
10. (Original post by Mr M)
That would be amazing! Thank you!

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