the integral of (X^3sin(6x)/sin(5x)) from -4 to 4
using the riemann sum as well?
post the answer if you know it.
I have been working on this for almost 4 hours now and can not figure it out.
Maybe you would care to reply with what work you have done and/or deadends that you have encountered in your four hours of work?
(edit)...
Having now looked at the actual integral.
The integrand is odd, integrated over an interval centered at zero. You might not be expected to find an antiderivative, but rather an analytic argument for why this integral equals...
My initial impression is, "This is an eyeball problem. The value of the integral is zero (0), by inspection. The argument is an odd function and the limits are symmetric about the origin."
A little more thought suggests I should determine that it actually exists. That sin(5x) in the denominator needs some thought. What do you think about it?
$\displaystyle x = 0, \frac{\pi}{5} + \frac{k\cdot\pi}{5}\;for\;k = \pm 1, 2, 3, 4, 5$
In x=0 the function has a removable singularity [You can easily verify that using l'Hopital rule...] and therefore that has no effects on integrability. Unfortunately in $\displaystyle [-4,4]$ there are several [non-removable...] singularities so that, according to the 'standard' definition, the integral doesn't exist. If we use however the definition of 'Cauchy Principal Value Integral'...
Cauchy Principal Value -- from Wolfram MathWorld
... and consider that f(x) is an odd function, the we can say that is...
$\displaystyle \text{P V} \int_{- a}^{a} f(x)\ dx =0$
Marry Christmas from Serbia
$\displaystyle \chi$ $\displaystyle \sigma$