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Find the area of the region bounded by the lines $x-y=1 $ and $x$-axis,$x=-2$ and $x=0$

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  • Area bounded by the curve $t=f(x),$ the x-axis and the ordinates $x=a,x=b$ is $\int \limits_a^b f(x) dx $ or $ \int \limits _a^b y dx $
  • If the curve lies below the x-axis for $a \leq x \leq b,$ then the area is $\int \limits_a^b (-y) dx=\int \limits_a^b (-f(x))dx$
Area bounded by the line $x-y=1$ and $x-axis, x=-2,x=0$
$x-y=1=>y=x-1$
The required area lies on the -ve side of the y-axis
$\therefore A=\int \limits _{-2}^0 -y dx$
$\quad= \int \limits_{-2}^0 (1-x) dx$
$\quad=x- \large\frac{x^2}{2} \bigg]_{-2}^0$
$\quad= 0-\bigg[-2-\large\frac{4}{2}\bigg]$$=4\;sq.units$
answered Aug 15, 2013 by meena.p
 

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