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Home  >>  CBSE XII  >>  Math  >>  Integrals
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Evaluate the definite integral\[\int\limits_{-1}^1(x+1)dx\]

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1 Answer

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Toolbox:
  • $\int\limits_a^b f(x)dx= F(b)-F(a)$
  • $ \int x^ndx=\Large\frac{x^{n+1}}{n+1}+c$
Given $I=\int \limits_{-1}^1 (x+1)dx$
 
On itntegrating we get,
 
$ I=[\large\frac{x^2}{2}+x]$
 
Applying the limits we get
 
$ \bigg(\Large\frac{1^2}{2}+1 \bigg)-\bigg(\frac{(-1)^2}{2}+(-1)\bigg)$
 
$=\bigg(\frac{1}{2}+1\bigg)-\bigg(\frac{1}{2}-1\bigg)$
 
$=\frac{1}{2}+1-\frac{1}{2}+1=2$

 

answered Feb 10, 2013 by meena.p
 
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