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Help with integration

This is a frequent reason to why I am getting a number of questions wrong. It seems that my answer is not the same as the one on the mark scheme since I am going down a different path to them in order to simplify the questions to such a point that they are able to be integrated. However, I do think I am breaking the laws of maths which would be the cause of a wrong answer can someone please help and explain what I’ve done wrong here as although it’s a different route to the mark scheme I don’t see why it’s incorrect. Thanks in advance!!

https://www.dropbox.com/s/mz1nf6i5dq8gk2o/Photo%2019-03-2018%2C%2014%2009%2053.jpg?dl=0
Reply 1
Original post by DedeM9
This is a frequent reason to why I am getting a number of questions wrong. It seems that my answer is not the same as the one on the mark scheme since I am going down a different path to them in order to simplify the questions to such a point that they are able to be integrated. However, I do think I am breaking the laws of maths which would be the cause of a wrong answer can someone please help and explain what I’ve done wrong here as although it’s a different route to the mark scheme I don’t see why it’s incorrect. Thanks in advance!!

https://www.dropbox.com/s/mz1nf6i5dq8gk2o/Photo%2019-03-2018%2C%2014%2009%2053.jpg?dl=0

Hi, please post the original question and also to be clear please tell us what your final answer was and what the mark scheme answer was.
Reply 2
Original post by Notnek
Hi, please post the original question and also to be clear please tell us what your final answer was and what the mark scheme answer was.

My Final answer is line third from bottom. The question is the top line and this is what the mark scheme says: https://www.dropbox.com/s/1b***7gmx5doaji/Photo%2019-03-2018%2C%2014%2042%2017.jpg?dl=0
Reply 3
Original post by DedeM9
My Final answer is line third from bottom. The question is the top line and this is what the mark scheme says: https://www.dropbox.com/s/1b***7gmx5doaji/Photo%2019-03-2018%2C%2014%2042%2017.jpg?dl=0

That link didn't work. It looks like something in the URL has been replaced by b***.

Your handwriting isn't the easiest to read :smile:

In the third line it looks like you have

cosycosecy dy\displaystyle \int \frac{\cos y}{cosec y} \ dy

and you're saying this is equal to

coty dy\displaystyle \int \cot y \ dy

Have I read that correctly? If I have then this isn't correct.
Reply 4
Yeah I did, I think that’s my problem it equals sin y doesn’t it. And then do I integrate that with the double angle formula?
Reply 5
Original post by DedeM9
Yeah I did, I think that’s my problem it equals sin y doesn’t it.

No.

cosycosecy=cosy÷1siny=cosy×siny=cosysiny\displaystyle \frac{\cos y}{cosec y} = \cos y \div \frac{1}{\sin y} = \cos y \times \sin y = \cos y \sin y

You can integrate cosysiny\cos y \sin y by using recognition or a sin/cos subsitution or by using the sin2A\sin 2A identity.

Also, I'm not sure how you got 2cos2x2\cos^2 x on the other side of the equation. You need to be careful when simplifying trig fractions - it often makes things easier if you write the fraction out using the ÷\div sign like I did above.
Reply 6
Original post by Kushala Daora
x

The TSR maths forum doesn't work in the app :smile:
Reply 7
Alright thanks for the help bud

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