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integrate tan^3(x/4)*sec^2(x/4) from2/3pi to pi
help with the steps plz.
 2 years ago
 2 years ago
integrate tan^3(x/4)*sec^2(x/4) from2/3pi to pi help with the steps plz.
 2 years ago
 2 years ago

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amistre64Best ResponseYou've already chosen the best response.0
since sec^2 is the derivaive of tan, this is a simple enough arrangement: \[\int f(u)du\]
 2 years ago

amistre64Best ResponseYou've already chosen the best response.0
i thinkk you might be off by a 4 tho
 2 years ago

amistre64Best ResponseYou've already chosen the best response.0
x/4 pops out a spurious little 1/4 that missing
 2 years ago

shinigami1mBest ResponseYou've already chosen the best response.1
is 2pi/3 to pi = to pi to 2pi/3 ???
 2 years ago

amistre64Best ResponseYou've already chosen the best response.0
then given the interval [a,b] you work it out: F(b)F(a)
 2 years ago

shinigami1mBest ResponseYou've already chosen the best response.1
dw:1326817635699:dw
 2 years ago

amistre64Best ResponseYou've already chosen the best response.0
\[[tan^4(\frac{1}{4}x)]'=\frac{1}{4}tan^3(\frac{1}{4}x)sec^2(\frac{1}{4}x)\] so we have to multiply thru by 4 to begin with
 2 years ago

amistre64Best ResponseYou've already chosen the best response.0
dw:1326817802065:dw
 2 years ago

TuringTestBest ResponseYou've already chosen the best response.1
\[u=\frac{x}{4}\to du=\frac{dx}{4}\to4du=dx\]\[\int_0}{dw:1326817852162:dw
 2 years ago

suju101Best ResponseYou've already chosen the best response.0
\[\Pi ^{2}\div9{(65\Pi ^{2}/9)26)}\] i got this ans. s this correct??i
 2 years ago

amistre64Best ResponseYou've already chosen the best response.0
lol, I just derived tan^4(x/4) and got a spurious 1/4 so that cant be right
 2 years ago

amistre64Best ResponseYou've already chosen the best response.0
hmmm, im off by something
 2 years ago

amistre64Best ResponseYou've already chosen the best response.0
wolf agrees with turing
 2 years ago

amistre64Best ResponseYou've already chosen the best response.0
oh yeah, the 4 pops out to get rid of the 1/4 lol
 2 years ago

shinigami1mBest ResponseYou've already chosen the best response.1
derivative of (x/4) i think u miss it during derivative
 2 years ago

TuringTestBest ResponseYou've already chosen the best response.1
yep, one comes out on top and bottom, so they cancel
 2 years ago

amistre64Best ResponseYou've already chosen the best response.0
a was using an abacus ;)
 2 years ago

suju101Best ResponseYou've already chosen the best response.0
dw:1326818150512:dw i did this process n got that ans
 2 years ago

TuringTestBest ResponseYou've already chosen the best response.1
is the problem\[\int_{\frac{2\pi}{3}}^{\pi}\tan^3(\frac x4)\sec^2(\frac x4)dx\]?
 2 years ago

TuringTestBest ResponseYou've already chosen the best response.1
\[\int_{\frac{2\pi}{3}}^{\pi}\tan^3(\frac x4)\sec^2(\frac x4)dx\]\[u=\frac x4\to du=\frac{dx}{4}\to4du=dx\]so...\[\int_{\frac{2\pi}{3}}^{\pi}\tan^3(\frac x4)\sec^2(\frac x4)dx=4\int_{\frac{\pi}{6}}^{\frac{\pi}{4}}\tan^3u\sec^2udu=4(\frac14\tan^4(\frac x4))_{\frac{2\pi}{3}}^{\pi}\]\[=\tan^4(\frac x4)_{\frac{2\pi}{3}}^{\pi}\]evaluate...
 2 years ago

robtobeyBest ResponseYou've already chosen the best response.2
\[\text{Tan}\left[\frac{\pi }{4}\right]^4\text{Tan}\left[\frac{\frac{2}{3}\pi }{4}\right]^4=\frac{8}{9} \]
 2 years ago
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