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# The area bounded by the line $y=x,$ the $x$-axis,the ordinates $x=1,x=2$ is

$\begin{array}{1 1}(1)\frac{3}{2}&(2)\frac{5}{2}\\(3)\frac{1}{2}&(4)\frac{7}{2}\end{array}$

$Area =\int \limits _1^2 y dx$
$\qquad= \int x dx = \large \frac{x^2}{2} \bigg]_1^2$
$\qquad= \large\frac{1}{2}$$[2^2-1^2] \qquad= \large\frac{1}{2}$$[4-1]$
$\qquad= \large\frac{3}{2}$
Hence 1 is the correct answer.