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TheBabe Group TitleBest ResponseYou've already chosen the best response.1
all right, \[\sin^3(2x)\]
 3 years ago

TheBabe Group TitleBest ResponseYou've already chosen the best response.1
seems like i need to do substitution rule, then use trig identities?
 3 years ago

LeoMessi Group TitleBest ResponseYou've already chosen the best response.1
right, let \[u=2x\], so \[du = 2 dx\], so \[dx=(1/2)du\]
 3 years ago

TheBabe Group TitleBest ResponseYou've already chosen the best response.1
\[\int\limits_{}^{}\sin^3 x\]
 3 years ago

LeoMessi Group TitleBest ResponseYou've already chosen the best response.1
forgot the dx ;), so that is equal to \[(1/2)\int\limits_{}^{}\sin^3(u)du\]
 3 years ago

LeoMessi Group TitleBest ResponseYou've already chosen the best response.1
\[sin^2x=1cos^2x\], so we'll have \[(1/2)\int\limits_{}^{}\sin^3(u)du\] = \[(1/2)\int\limits_{}^{}\sin^2(u)*sin(u)du\] = \[(1/2)\int\limits_{}^{}(1sin^2(u))sin(u)du\]
 3 years ago

LeoMessi Group TitleBest ResponseYou've already chosen the best response.1
so we can apply substitution rule again for \[v=\sin(u)\]
 3 years ago

LeoMessi Group TitleBest ResponseYou've already chosen the best response.1
\[dv = \cos(u)du\], so \[(1/2)\int\limits_{}^{}(1v^2)dv\]
 3 years ago

TheBabe Group TitleBest ResponseYou've already chosen the best response.1
wait, shouldn't it be 1cos^2(u) above?
 3 years ago

LeoMessi Group TitleBest ResponseYou've already chosen the best response.1
ahhh, yesss... sorry: \[(1/2)\int\limits_{}^{}(1cos^2(u))sin(u)du\]
 3 years ago

TheBabe Group TitleBest ResponseYou've already chosen the best response.1
so v=cos(u), which is dv=sin(u)du
 3 years ago

TheBabe Group TitleBest ResponseYou've already chosen the best response.1
i think I got it now: so\[(1/2)\int\limits\limits_{}^{}(1\cos^2(u))\sin(u)du = (1)*(1/2) \int\limits_{}^{} (1v^2)dv = (1)(1/2) [ v(1/3)v^3 + C]\]
 3 years ago

TheBabe Group TitleBest ResponseYou've already chosen the best response.1
i think I got it now: so\[(1/2)\int\limits\limits_{}^{}(1\cos^2(u))\sin(u)du\] = \[(1)*(1/2) \int\limits_{}^{} (1v^2)dv\] = \[(1)(1/2) [ v(1/3)v^3 + C]\]
 3 years ago

TheBabe Group TitleBest ResponseYou've already chosen the best response.1
so plug back in and get v = cos u > cos (2x), \[(1)(1/2) [ v(1/3)v^3 + C] = (1)(1/2) [ \cos(2x)  (1/3)\cos^3(2x) + C]\] \[ = (1)(1/2) [ cos(2x)  (1/3)cos^3(2x) + C]\]
 3 years ago
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