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

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ganeshie8
 10 months ago
Best ResponseYou've already chosen the best response.0even/odd stuff ha ?

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

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

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

hartnn
 10 months 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

hartnn
 10 months ago
Best ResponseYou've already chosen the best response.3did u get what to do ?

klimenkov
 10 months 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
 10 months 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
 10 months 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
 10 months 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
 10 months 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
 10 months 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
 10 months ago
Best ResponseYou've already chosen the best response.3i am NOT doing any substitution

klimenkov
 10 months 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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