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# C4 maths doubt! watch

1. Hello there,
Have they got an error on here? Question No. 7 part a of the question . Was that meant to be -4? thanks!

http://www.london-oratory.org/maths/...s/E4Qint_P.pdf
2. (Original post by laurawoods)
Hello there,
Have they got an error on here? Question No. 7 part a of the question . Was that meant to be -4? thanks!

http://www.london-oratory.org/maths/...s/E4Qint_P.pdf
No, 4 is correct, You're trying to find an area which is positive.

If you look at the integral they've given, everything in it is positive, so the answer will be positive. If you had a -4 you would be getting a negative answer.

check the limits on your integral and make sure you have them the right way round
3. (Original post by laurawoods)
Hello there,
Have they got an error on here? Question No. 7 part a of the question . Was that meant to be -4? thanks!

http://www.london-oratory.org/maths/...s/E4Qint_P.pdf
hahah you stress me out with your posts about Alevels all the time
4. (Original post by laurawoods)
Hello there,
Have they got an error on here? Question No. 7 part a of the question . Was that meant to be -4? thanks!

http://www.london-oratory.org/maths/...s/E4Qint_P.pdf
No, 4 is correct.

When you have a negative integral you can switch the limits and make it positive.
5. (Original post by davros)
No, 4 is correct, You're trying to find an area which is positive.

If you look at the integral they've given, everything in it is positive, so the answer will be positive. If you had a -4 you would be getting a negative answer.

check the limits on your integral and make sure you have them the right way round
sorry i don't think I am understanding this! When we initially write down we get (y) * (dx/dt) = -4sin^2t

Isn't it so?

And also where did they get pi/4 and 0 from ? are we meant to work that out ourselves or simply take that from the answer they have given? thanks for your help!
6. (Original post by laurawoods)
sorry i don't think I am understanding this! When we initially write down we get (y) * (dx/dt) = -4sin^2t

Isn't it so?

And also where did they get pi/4 and 0 from ? are we meant to work that out ourselves or simply take that from the answer they have given? thanks for your help!

Remember when you integrate to work out an area you're going from the leftmost x-value to the rightmost x-value.

In your graph, the leftmost x-value is 0 at the point O, so your bottom limit of integration is the value of t that makes x=0.

At the rightmost point (call it P) you know that y=0. So what value of t makes y=0? This gives you the top limit of integration.

Then note that when you have a minus sign in the function you're integrating you can convert this to a positive sign by swapping the limits of the integral round. This should get you to something that looks like the answer!
7. (Original post by davros)

Remember when you integrate to work out an area you're going from the leftmost x-value to the rightmost x-value.

In your graph, the leftmost x-value is 0 at the point O, so your bottom limit of integration is the value of t that makes x=0.

At the rightmost point (call it P) you know that y=0. So what value of t makes y=0? This gives you the top limit of integration.

Then note that when you have a minus sign in the function you're integrating you can convert this to a positive sign by swapping the limits of the integral round. This should get you to something that looks like the answer!
Hello, I think I get it now! thanks for the answer! these limits are driving me mad :>
8. (Original post by laurawoods)
Hello, I think I get it now! thanks for the answer! these limits are driving me mad :>
no problem!
9. (Original post by davros)
no problem!
Hello , pls can I ask a quick question :
When we have an exponential equation and they ask us for the long term speed etc is it the value that comes like "+C" for example :
V = -5e^-1/5t + 60

so would the long term value be the 60 ? is this always the case?
10. Yay Maths
11. )
(Original post by laurawoods)
Hello , pls can I ask a quick question :
When we have an exponential equation and they ask us for the long term speed etc is it the value that comes like "+C" for example :
V = -5e^-1/5t + 60

so would the long term value be the 60 ? is this always the case?
Yes if you've got a negative exponential like that - as t gets bigger and bigger, gets smaller and smaller if k>0, so the total value gets closer and closer to the constant (in this case 60).

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