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Home  >>  CBSE XII  >>  Math  >>  Integrals
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Integrate the function\[\cot x\;log \sin x\]

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Toolbox:
  • Method of substitution :
  • Given f(x)dx can be transformed into another form by changing independent variable x to t by substituting x=g(t).
  • Consider $I=\int f(x)dx.$
  • Put x=g(t) so that $\frac{dx}{dt}=g'(t).$
  • $\Rightarrow $dx=g'(t)dt.
  • Thus $I=\int f(g(t).g'(t))dt.$
Given $I=\int \cot xlog \sin x.$
 
Put $log \sin x=t\quad[\frac{1}{\sin x}.\cos xdx=dt=\cot x].$
 
Now substituting for x and dx we get,
 
$I=\int t dt.$
 
On integrating we get,
 
$\frac{t^2}{2}+c.$
 
Substituting back for t we get,
 
$\int \cot xlog \sin xdx=\frac{1}{2}(log sin x)^2+c.$
 
 

 

answered Jan 29, 2013 by sreemathi.v
edited Jan 29, 2013 by sreemathi.v
 
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