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

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BSwan
 one year ago
Best ResponseYou've already chosen the best response.02014 is order of derivative ?

hartnn
 one year 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
 one year ago
Best ResponseYou've already chosen the best response.1@BSwan 2014 is the power.

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

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

klimenkov
 one year 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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