summaryrefslogtreecommitdiffstats
diff options
context:
space:
mode:
-rw-r--r--Problem Set 2.page2
1 files changed, 1 insertions, 1 deletions
diff --git a/Problem Set 2.page b/Problem Set 2.page
index 2d5a503..667abad 100644
--- a/Problem Set 2.page
+++ b/Problem Set 2.page
@@ -41,7 +41,6 @@ $\int_0^{2\pi} |\sin^2(x)|^2 dx = \sum |a_n|^2.$
2. Since
$\sin x = \frac{e^{ix}-e^{-ix}}{2}$,
-
$\sin^4 x = \frac{{( e^{ix}-e^{-ix} )}^4}{16}$
$= \frac{e^{i 4x}+e^{-i 4x}-4 e^{i 2x} -4 e^{-i 2x}+6}{16}$.
@@ -56,6 +55,7 @@ $a_{-4} = a_{4} = \sqrt{2\pi} \times 1/16$, $a_{-2} = a_{2} = - \sqrt{2\pi} \tim
Since $a_m = < f_m, f >$,
+
$\int_0^{2\pi} \sin^4(x) dx = <1, f> = \sqrt{2\pi} \times < f_0, f >$
$= \sqrt{2\pi} \times a_0 = \frac{3 \pi}{4}$