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klimenkov
 2 years ago
\[\int_{\frac{\pi}2}^{\frac{\pi}2} \frac{\sin^{2014}x}{\sin^{2014}x + \cos^{2014}x} \, dx\]
klimenkov
 2 years ago
\[\int_{\frac{\pi}2}^{\frac{\pi}2} \frac{\sin^{2014}x}{\sin^{2014}x + \cos^{2014}x} \, dx\]

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anonymous
 2 years ago
Best ResponseYou've already chosen the best response.02014 is order of derivative ?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3\(\Large \int_a^b f(x) dx= \int_a^bf(a+bx)dx \) use this!

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1@BSwan 2014 is the power.

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3after you have proved that your function is even

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3\(\Large \int_{a}^a f(x) dx = 2\int_0^a f(x)dx\) if f(x) is even function

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1\[2\int\limits_0^{\frac{\pi}2} \frac{\sin^{2014}x}{\sin^{2014}x + \cos^{2014}x} \, dx\]What's next?

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3\(\Large \int_a^b f(x) dx= \int_a^bf(a+bx)dx\) replace x by pi/2  x

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3\(I = 2\int\limits_0^{\frac{\pi}2} \frac{\sin^{2014}x}{\sin^{2014}x + \cos^{2014}x} \, dx ... ... (A)\) just giving a label, to be used later

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1\[2 \int\limits_0^{\frac{\pi}2} \frac{\cos^{2014}x}{\sin^{2014}x + \cos^{2014}x} \, dx\]

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3\(I = 2 \int\limits_0^{\frac{\pi}2} \frac{\cos^{2014}x}{\sin^{2014}x + \cos^{2014}x} \, dx ... ... (B)\) Add (A) and (B)

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1\[I = 2 \int\limits_0^{\frac{\pi}2} \frac{\cos^{2014}x}{\sin^{2014}x + \cos^{2014}x} \, dx\]

hartnn
 2 years ago
Best ResponseYou've already chosen the best response.3i am NOT doing any substitution

klimenkov
 2 years ago
Best ResponseYou've already chosen the best response.1Yeah, everything is okay. My fault. \[I + I = 2\int_0^{\frac\pi2}dx,\]\[I=\frac\pi2.\]Very nice, thank you.
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