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Find the area of the region bounded by the lines $x-y=1 $ and $x$-axis,$x=2$ and $x=4$

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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 $x-axis, x=2,x=4$
$x-y=1=>y=x-1$
$A=\int \limits_2^4 y dx$
$\quad= \int \limits_2^4 (x-1) dx$
$\quad= \large\frac{x^2}{2}$$-x \bigg]_2^4$
$\quad= (8-4)-(2-2)$
$\quad= 4\;sq \;units$
answered Aug 15, 2013 by meena.p
 

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