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

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

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

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

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

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

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

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

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

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

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

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