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Home  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus

Integrate :$\int \limits_0^3 |2-x|\;dx$

\[\begin {array} {1 1} (a)\;\frac{3}{2} \\ (b)\;\frac{5}{2} \\ (c)\;\frac{7}{2} \\ (d)\;\frac{1}{2} \end {array}\]

1 Answer

At $x=2$ equation will be zero.
By graphical met at $x=0,y=2$
$x=3,y=1$
$-(2-x) x >2$
=> $\int\limits_0^2 (2-x)dx +\int \limits _2^3 -(2-x) dx$
=> $ \bigg[2x-\large\frac{x^2}{2}\bigg]_0^2$$- \int 2x -\large\frac{x^2}{2} \bigg]_2^3$
=> $[4-2]- [6-\large\frac{g}{2}$$-4+2]$
=> $ 2 - [-\large\frac{1}{2}]=\frac{5}{2}$
Hence b is the correct answer.
answered Dec 13, 2013 by meena.p
 
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