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lambchamps
Group Title
int. calculus
\[\int\limits_{}^{}\sin ^{2}x \cos ^{2}x \tan ^{2} x dx\]
 2 years ago
 2 years ago
lambchamps Group Title
int. calculus \[\int\limits_{}^{}\sin ^{2}x \cos ^{2}x \tan ^{2} x dx\]
 2 years ago
 2 years ago

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Freak7820 Group TitleBest ResponseYou've already chosen the best response.0
Write them as sin squared x = (1/2)(1  cos 2x) cos squared x = (1/2)(1 + cos 2x) maybe..that'll be easier for you to integrate.
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.0
can i do that, even if sin or cos is not raised two?
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
doesn't that simplify to sin^4 x when tan is written as sin/cos ?
 2 years ago

SheldonEinstein Group TitleBest ResponseYou've already chosen the best response.3
Write tan^2 x = sin^2 x / cos^2 x
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.0
i did that before
 2 years ago

SheldonEinstein Group TitleBest ResponseYou've already chosen the best response.3
\[\large{\int { sin^4x dx}}\] Can you do this?
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.0
then i lost any of ideas after that
 2 years ago

SheldonEinstein Group TitleBest ResponseYou've already chosen the best response.3
OK no problem, where are you lost?
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
can u integrate sin^2 x ?
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.0
after i got the \[\int\limits_{?}^{?}\sin ^{4}xdx\]
 2 years ago

SheldonEinstein Group TitleBest ResponseYou've already chosen the best response.3
Well if integration of sin x dx= cosx + C then that of sin^4 x dx = ?
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.0
cos^4x + C ??
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
write sin^4 x = (sin^2 x)(1cos^2 x)
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
no, its not that direct
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.0
then distribute?
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
= (sin^2 x)(1cos^2 x) = sin^2 x  sin^2x cos^2 x yes
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
= sin^2 x  sin^2x cos^2 x = sin^2 x  (1/4) (sin 2x)^2
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.0
how did you get (1/4)(sin 2x)^2?
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
sin 2x = 2 sin x cos x to get sin^2x cos^2 x , i squared the above .....
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
got that ? ^ and can u integrate sin^2 x  (1/4) (sin 2x)^2
 2 years ago

lambchamps Group TitleBest ResponseYou've already chosen the best response.0
can you show me the whole process of that sin 2x = 2 sin x cos x
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
u want me to prove 2sin x cos x = sin 2x or u wanted this : sin 2x = 2 sin x cos x (sin 2x)^2 = (2 sin x cos x)^2 = 4 sin^2x cos^2 x so sin^2 x cos^2 x = (1/4) (sin 2x)^2
 2 years ago

hartnn Group TitleBest ResponseYou've already chosen the best response.2
so if u can integrate sin^2 x you can also integrate sin^2 x  (1/4) (sin 2x)^2
 2 years ago
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