Recent content by benjyk

Yes they do :) Thanks again for the help.

I have to admit I am a little disappointed. I thought there might be a way of performing the integral by pure analytical means. But thank you very much for your responses.

I am trying to calculate the arc length of a sine wave. Using s=\int_{}^{}\sqrt[]{1 + {(\frac{dy}{dx})}^{2}}dx if y = sinx, dy/dx = cosx So the integral simplyfies to s=\int_{}^{}\sqrt[]{1 + {cos}^{2}(x)}dx However I do not know any integration technique (ie. substitution, by parts...

Thanks for your reply Avodyne. To solve it, I expressed cos^2n(theta) as (z + z^-1)^2n. This expanded to yield: (cos(2n) + 2nC1*cos(2n-2) + ... + (2n)!/(n1)^2) / 2^2n When integrated, all the cos's become sin's. The sine of zero or any integer multiple of 2pi will cancell, therefore the...

Homework Statement Show that \int_{0}^{\pi} {\cos}^{2n}\theta d\theta = \frac{(2n)!\pi}{{2}^{2n}{(n!)}^{2}} Homework Equations cos n*theta = (z^n + z^-n)/2 The Attempt at a Solution Ok, this one has kept me busy for a while. I started using de Moivre's theorem to express...

This may come in handy.. log(a/b)=log(a)-log(b)

I would multiply both sides by (8-4sin(theta)) and then you can replace rsin(theta) with y. And then you can use your identity r^2 = x^2 + y^2.

Thank you very much for your reply. After an hour of frustrating and sadly unfruitful algebraic manipulation, I am still no closer to the answer of sin(2nx) / 2sin(x). Any further help would be greatly appreciated.

Let u = ln x and dv/dx = x^-3 and use integration by parts. And see what happens as the upper bound of the integral tends to infinity.

Homework Statement Use cos ( n * x) = (z ^ n + z ^ -n)/2 to express cos x + cos 3x + cos 5x + ... + cos([2n -1]x) as a geometric series in terms of z. Hence find this sum in terms of x Homework Equations The Attempt at a Solution (z + z^-1)/2 + (z^3 + z^-3)/2 + ... +...