From 69d07c77b0de12a2d268418f9a67395280a730c4 Mon Sep 17 00:00:00 2001 From: joshuab <> Date: Wed, 30 Jun 2010 19:46:02 +0000 Subject: trying to fix ints --- Problem Set 1.page | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) (limited to 'Problem Set 1.page') diff --git a/Problem Set 1.page b/Problem Set 1.page index eb2c6e7..eb0a758 100644 --- a/Problem Set 1.page +++ b/Problem Set 1.page @@ -25,10 +25,10 @@ Cook up other examples and post them on the wiki! - $g(x) = x(x-2\pi)$ (Hint: Use integration by parts) 2. Show that -$ \int_0^{2\pi} sin^4(x) dx = \frac{3 \pi}{4} $ +$\int_0^{2\pi} sin^4(x) dx = \frac{3 \pi}{4} $ (Hint: write out the exponential fourier expansion of $sin^4(x)$.) 3. Compute the exponential Fourier coefficients of $sin^2(x)$: -$ a_n = \frac{1}{\sqrt(2\pi)} \int_0^{2\pi} sin^2(x) e^{-inx} dx $ +$a_n = \frac{1}{\sqrt(2\pi)} \int_0^{2\pi} sin^2(x) e^{-inx} dx $ and use this to show that -$ \int_0^{2\pi} |sin^2(x)|^2 dx = \sum |a_n|^2 $ +$\int_0^{2\pi} |sin^2(x)|^2 dx = \sum |a_n|^2 $ -- cgit v1.2.3