Homework Problem on Integration

Asked Apr 19 '17 at 10:01

Active Apr 19 '17 at 12:10

Viewed 48 times

$g(x)= \tan(x)+ 2\tan 2x + 4\tan 4x + 8\cot 8x$

and $f(x) = (7\tan^{6} x -3\tan^{2} x) \dfrac{1}{g^{2}(x)+1}$;

$x \in \left( 0,\dfrac{\pi}{4} \right)$

Then find $\displaystyle \int_0^\frac{\pi}{4} f(x) dx$ and $\displaystyle \int_0^\frac{\pi}{4} xf(x) dx$

Basically, I don't know how to simplify $f(x)$ or substitute anything.

edited Apr 19 '17 at 12:10

Ng Chung Tak

asked Apr 19 '17 at 10:01

Abhash Jha

1

Check whether I have wrongly edited something. – Archis Welankar Apr 19 '17 at 10:06
See https://math.stackexchange.com/questions/2125682/to-prove-tana-2-tan2a-4-tan4a-8-cot8a-cota – lab bhattacharjee Apr 19 '17 at 10:07
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i have simplified your term as $${\frac { \left( 4, \left( \cos \left( x \right) \right) ^{4}-14, \left( \cos \left( x \right) \right) ^{2}+7 \right) \left( \sin \left( x \right) \right) ^{4}}{ \left( \cos \left( x \right) \right) ^{6}}} $$ – Dr. Sonnhard Graubner Apr 19 '17 at 10:13
is your Problem solved now? – Dr. Sonnhard Graubner Apr 19 '17 at 10:21
i got $\int_0^\frac{\pi}{4} tan^{4}x sec^{2}{x} \frac{7tan^{4}{x} - 3}{(1+tan^{2}{x})^2} dx$ – Abhash Jha Apr 19 '17 at 10:46

0 Answers0