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Find the area of the region bounded by the lines $x-2y-12=0$ and $y$-axis,$y=2$ and $y=5$

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Toolbox:
• 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 $x-2y-12=0$ and $y-axis,y=2,y=5$
$x-2y-12=0=>x=2y+12$
$A=\int \limits _{2}^5 x dy$
$\quad=\int \limits _{2}^5 (2y+12)dy$
$\quad=y^2+12y \bigg]_{2}^5$
$\quad=(25+60)-(4+24)$
$\quad=85-28=57 \;sq.units$
answered Aug 15, 2013 by