You are Here: Home >< Maths

# FP2 Integral Watch

1. Find the integral of 1/(x^2+1)^2
2. (Original post by MEPS1996)
Find the integral of 1/(x^2+1)^2
What substitutions do you know that might help you? What would you do if the denominator were just (x^2 + 1)?
3. (Original post by davros)
What substitutions do you know that might help you? What would you do if the denominator were just (x^2 + 1)?
of course x=tan(t) substitution thanks
4. (Original post by MEPS1996)
...
Alternatively, you could opt for the substitution
5. (Original post by Khallil)
Alternatively, you could opt for the substitution
Hey, I just wanted to ask a general question (couldn't find another FP2 thread).

When finding the area of a cardioid, how do I find out what the limits are, directly from the r= equation?
6. (Original post by TheAsian)
...
I'd presume so. It's been a while since I've looked at polar coordinates. Do you have an example with which I can work?

Also, so that we don't derail the primary purpose of this thread, perhaps you could send me a VM (visitor message)?
7. (Original post by Khallil)
I'd presume so. It's been a while since I've looked at polar coordinates. Do you have an example with which I can work?
"find the area of a single loop of the curve with equation r = acos3x"

The limits are pi/6 and -pi/6 but im not sure how they got that? thank you
8. (Original post by TheAsian)
"find the area of a single loop of the curve with equation r = acos3x"

The limits are pi/6 and -pi/6 but im not sure how they got that? thank you
This is going to be a tough one to explain.

Before looking at the polar curve, a very brief glance at the Cartesian trigonometric curve should give you a better idea of what is going on. For a loop to exist in the very first place, the endpoints of the region of the angle you're looking at must give a zero value for . In this case, you could choose the region of as the arrow I drew parallel to the axis. Now it's just a matter of concerning yourself only with the positive values of (as most exam boards don't bother with -ve values) for which the endpoints are equal to 0.

(I couldn't get Wolfram to graph the output as )
In this respect, you could equally find the the integral and you'd get the same area.
9. (Original post by Khallil)
This is going to be a tough one to explain.

Before looking at the polar curve, a very brief glance at the trigonometric curve should give you a better idea of what is going on. For a loop to exist in the very first place, the endpoints of the region of the angle you're looking at must give a zero value for . That much should be clear. Now it's just a matter of concerning yourself only with the positive values of (as most exam boards don't bother with -ve values) for which the endpoints are equal to 0.

(I couldn't get Wolfram to graph the output as )
In this respect, you could equally find the the integral and you'd get the same area.
oh, okay! that's a lot clearer now, thank you vm!
10. (Original post by TheAsian)
oh, okay! that's a lot clearer now, thank you vm!
No prob. I edited a bit of my reply to make the "region of x for which the loop is enclosed" bit a tad clearer :-)
11. (Original post by Khallil)
No prob. I edited a bit of my reply to make the "region of x for which the loop is enclosed" bit a tad clearer :-)
it did clarify, thank you
12. (Original post by MEPS1996)
Find the integral of 1/(x^2+1)^2
I figured the question asked might be of some use to you too, so I posted my reply a few posts above.

(Original post by TheAsian)
it did clarify, thank you
Nice question! Out of curiosity, did you get your final area as ?
13. (Original post by Khallil)
Nice question! Out of curiosity, did you get your final area as ?
yes! after finding the limits, it's really easy to do
14. (Original post by TheAsian)
yes! after finding the limits, it's really easy to do
Somebody's confident
15. (Original post by Khallil)
Somebody's confident
far from it, further maths is my scariest pursuit as of yet

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: April 17, 2014
Today on TSR

### Should I hide my grades on UCAS?

I don't want Oxford to know I only got an A...

### He wants to drop out of Cambridge?

Discussions on TSR

• Latest
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams