I'm bored. Give me a challenging maths problem to work on.

No, but a mature person wouldn't stick rainbow colours on their profile picture, would they? You'd look older without them..

ANYWAY; DOES ANYBODY HAVE OTHER DECENT MATHS PROBLEMS?

Poor @ivybridge and all those people on FB with their rainbow profile pictures...so many 14 year olds

And poor you for thinking the animated non existent person in my profile picture is me. Embarrassing.

Yeah

Try STEP (Sixth Term Examination Papers in Mathematics)
You can find past papers and Siklos booklets online for free

Go away; you don't belong here.

I did this problem in my STEP exam this summer. It's really good fun and I'm sure you'll enjoy it.

Given that;

$sec^2 \bigg( \dfrac{1}{4} \pi - \dfrac{1}{2}x \bigg) = \dfrac{2}{1 + sin(x)}$

and

$\displaystyle \int_{0}^{\pi} xf(sinx) dx = \dfrac{\pi}{2} \displaystyle \int_{0}^{\pi} f(sinx) dx$


Evaluate $\displaystyle \int_{0}^{\pi} \dfrac{x}{1+ sinx} dx$


and $\displaystyle \int_{0}^{\pi} \dfrac{2x^3 - 3 \pi x^2}{(1+ sinx)^2} dx$

A-levelish.

You try to pick a fight, you get knocked down, little boy.

Question 10. Hints?

Question 10. Hints?

I did it by a substitution; there may be a quicker way. Express 2x^2 + 4x + 3 in terms of (x + 1)^2 and the kind of substitution to do might jump out at you.

I did it by a substitution; there may be a quicker way. Express 2x^2 + 4x + 3 in terms of (x + 1)^2 and the kind of substitution to do might jump out at you.

Thanks. For 10, what's the suitable, non-trigonometric substitution?
I tried integration by parts, but 20 minutes later and I'm nowhere.

Do you mean 9b?

yes.

No, but a mature person wouldn't stick rainbow colours on their profile picture, would they? You'd look older without them..

ANYWAY; DOES ANYBODY HAVE OTHER DECENT MATHS PROBLEMS?

Use proof by induction to prove the Maclaurin's Series of $tanh^(-1) x$