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

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ganeshie8 Group TitleBest ResponseYou've already chosen the best response.0
even/odd stuff ha ?
 one month ago

BSwan Group TitleBest ResponseYou've already chosen the best response.0
2014 is order of derivative ?
 one month ago

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

klimenkov Group TitleBest ResponseYou've already chosen the best response.1
@BSwan 2014 is the power.
 one month ago

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

BSwan Group TitleBest ResponseYou've already chosen the best response.0
aha cool :)
 one month ago

hartnn Group TitleBest 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
 one month ago

hartnn Group TitleBest ResponseYou've already chosen the best response.3
did u get what to do ?
 one month ago

klimenkov Group TitleBest 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?
 one month ago

hartnn Group TitleBest 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
 one month ago

hartnn Group TitleBest 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
 one month ago

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

klimenkov Group TitleBest ResponseYou've already chosen the best response.1
Oops...
 one month ago

hartnn Group TitleBest 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)
 one month ago

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

hartnn Group TitleBest ResponseYou've already chosen the best response.3
what ? why negative ?
 one month ago

hartnn Group TitleBest ResponseYou've already chosen the best response.3
dx remains as dx
 one month ago

hartnn Group TitleBest ResponseYou've already chosen the best response.3
i am NOT doing any substitution
 one month ago

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

hartnn Group TitleBest ResponseYou've already chosen the best response.3
welcome ^_^
 one month ago
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