1. ## Maths for Physics

Hey Guys can you give me some guiding points for a few questions. Trying to refresh myself with doing this kind of work.

1 I) Find Integral of 1/(Cos^2(X)) and 1/(Sin^2(X))

II) Integrate Cos(X)+ [Sin(X)] DX with limits Pie and -Pie. I know the answer is 4 for this but can't get the working right.

III) Similarly Integrate ([u-1]+[u+1]) DU with limits 4 and -3.

With [] symbolosing postive squareroots.

Thanks for any help and apologies for the lay out but any help would be greatly appreciated.

2. ## Re: Maths for Physics

Hi, Mathsnewbie. I will try to point in the right direction on the first exercise of your post.

You may find that $\displaystyle \frac{1}{\sin(x)}=\csc(x)$ and $\displaystyle \frac{1}{\cos(x)}=\sec(x)$ are relevant. The table involving trig functions and their derivtives at Differentiation of trigonometric functions - Wikipedia, the free encyclopedia may also be of some use. I think this (along with the Fundamental Theorem of Calculus, i.e. taking antiderivatives) is enough to finish off the exercise.

If this is too cryptic let me know and I will try to be more explicit with my hints. Good luck!

3. ## Re: Maths for Physics

This is great thank you!

4. ## Re: Maths for Physics

No problemo. Were you able to get parts II and III?

5. ## Re: Maths for Physics

Originally Posted by Mathsnewbie
...
II) Integrate Cos(X)+ [Sin(X)] DX with limits Pie and -Pie ...
fyi, this is pi ...

... and this is pie

6. ## Re: Maths for Physics

I managed to get II but struggling with III at the moment.

7. ## Re: Maths for Physics

Good job! Keep at it, and if you're totally stumped I can send some thoughts that may put you back on course.

8. ## Re: Maths for Physics

Would I be right in saying 7 for part III)

My working is

Integral with limits 4,0 (u-1)+(u+1)du + Integral with limits 0,-3 (-u-1)+(-u+1)du

So I get Integral 2uDu + Integral -2uDu with limits 4,0 and 0.-3 respectively

Which equals (U)4,0 + (-U)0,3Which = 4-0 + (0-(-3) = 7