anonymous
  • anonymous
Evaluate the integral! From 0 to pi/3 of 4sec x tan x dx
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
\[\int\limits_{0}^{\pi/3} 4\sec x \tan x\]
anonymous
  • anonymous
i am helpi u right noe
anonymous
  • anonymous
Like i get the basic jist of integrals i just get stuck on finding the antiderivative

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anonymous
  • anonymous
oka
anonymous
  • anonymous
see if you can think of a function whose derivative is \(\sec(x)\tan(x)\)
anonymous
  • anonymous
or look in the book for the derivatives of trig functions. you will see it
anonymous
  • anonymous
i cant find the anser
anonymous
  • anonymous
sec 4x and they just applied the chasin rule?
anonymous
  • anonymous
chain*
anonymous
  • anonymous
easier than that
anonymous
  • anonymous
if you take the derivative of \(\sec(4x)\) you will get \(4\sec(4x)\tan(4x)\) which is not at all what you want. just leave the constant alone and take \(4\sec(x)\)
anonymous
  • anonymous
plug in \(\frac{\pi}{3}\) plug in \(0\) and subtract actually forget 0 because \(\tan(0)=0\)
anonymous
  • anonymous
ok perfect i can do it from here thanks :)
anonymous
  • anonymous
yw
anonymous
  • anonymous
answers 2 right?
anonymous
  • anonymous
yes

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