Provide a challenge! :)

Anyone got algebraic or system of equations challenge?!!

Using numerical integration techniques, 

\(\int _{-2}^2\left(x^3\cos \left(\frac{x}{2}\right)+\frac{1}{2}\right)\sqrt{4-x^2}dx\) would be \(\pi\)

Split the integral into two parts, so you have int(x³cos(x/2)sqrt(4-x²))dx + (1/2)int(sqrt(4-x²))dx

The kernel of the first integral is odd, so when integrating from -2 to +2, the result is zero.

For the second integral make the substitution x = 2theta, say, and it is a simple matter to find the result as pi.

Asker guest:

Please reinstate the original address.

If questions are repeats they should always be linked with the original.

Thanks Alan :)