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

Question

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

Answer 1

$Area =\int \limits _1^2 y dx$

$\qquad= \int x dx = \large \frac{x^2}{2} \bigg]_1^2$

$\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.