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C2 soloman paper B. integration with an infinate limity watch

1. Hey. Could somone help me with question 8(ii)

https://b940eb267c31463d4d23ccfd3105...20C2%20OCR.pdf

I dont understand how to deal with infinite limits.
thanks
2. (Original post by SamuelN98)
Hey. Could somone help me with question 8(ii)

https://b940eb267c31463d4d23ccfd3105...20C2%20OCR.pdf

I dont understand how to deal with infinite limits.
thanks

The := means defined as. You'd cover this in FP1 and FP3. You probably haven't been taught what a limit is or how to deal with them, but use the intuitive notion of b becoming infinitely large.
3. Consider first doing the Integral and you would get a result of

Now, for the infinite integral, replace it with some variable, for example for the meantime and then plug in both values to give . Now consider taking as . So that as tends to infinity, from before would get smaller and smaller so you can consider it as being zero. Therefore you would be left with your result of as your final answer.
4. hmmm i don't understand any of this xD but i'd like to understand :/
5. (Original post by thefatone)
hmmm i don't understand any of this xD but i'd like to understand :/
What happens to as gets really, really, really big? If you're not sure, keep plugging bigger numbers into your calculator, what value does it approach?
6. (Original post by Zacken)
What happens to as gets really, really, really big? If you're not sure, keep plugging bigger numbers into your calculator, what value does it approach?
it gets infinitely small
7. (Original post by thefatone)
it gets infinitely small
And if you had to give a value to it, what value would you give it?
8. (Original post by Zacken)
And if you had to give a value to it, what value would you give it?
the infinity symbol??

edit: 0?
9. (Original post by thefatone)
the infinity symbol??

edit: 0?
It gets infinitely small and you put the infinity symbol? ._.

0 is correct.

Knowing that, how would you integrate ?
10. (Original post by Zacken)
It gets infinitely small and you put the infinity symbol? ._.

0 is correct.

Knowing that, how would you integrate ?
of course xD

hmmm write it without a fraction? i.e ?
11. (Original post by thefatone)
of course xD

hmmm write it without a fraction? i.e ?
How do you integrate ?
12. (Original post by thefatone)
of course xD

hmmm write it without a fraction? i.e ?
The notation is equivalent to .
I suspect this is causing you some confusion . . .
13. (Original post by Zacken)
How do you integrate ?
well raise the power by 1 and divide by the new power

so the result would be

(Original post by joostan)
The notation is equivalent to .I suspect this is causing you some confusion . . .
yea just a little xD
14. (Original post by thefatone)
well raise the power by 1 and divide by the new power

so the result would be
Yes, so now with limits: - what do you get now?
15. (Original post by SamuelN98)
Hey. Could somone help me with question 8(ii)

https://b940eb267c31463d4d23ccfd3105...20C2%20OCR.pdf

I dont understand how to deal with infinite limits.
thanks
If you just integrate normally, and let X = infinite. Then when you come to your final answer with x's in it. You can take limits. So for example 2/X, as x turns to infitnite, 2/x =0.
16. (Original post by Zacken)
Yes, so now with limits: - what do you get now?
that's the bit i was unsure about....
actually

you get [0]-[-1] so the value is just 1?
17. (Original post by thefatone)
that's the bit i was unsure about....
actually

you get [0]-[-1] so the value is just 1?
Yeah, that's correct.
18. (Original post by Zacken)
Yeah, that's correct.
oh ok thanks a lot ^-^
19. (Original post by thefatone)
oh ok thanks a lot ^-^
No problem.
20. (Original post by Zacken)
No problem.

i integrated and got

then i put values in and got

[0]-[1.414]
so is -1.414 correct as an answer?

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