question_answer

The area of the region bounded by the curve\[y=\frac{3}{{{x}^{2}}},\]\[x-\]axis and\[x=1,\text{ }x=2\]is

A)  \[1\,sq\,unit\]

B)  \[3\,sq\,unit\]

C)  \[2\,sq\,unit\]

D)  \[\frac{3}{2}\,sq\,unit\]

Correct Answer: D

Solution :

 Required area\[=\int_{1}^{2}{y\,dx}=\int_{1}^{2}{\frac{3}{{{x}^{2}}}}dx\] \[=3\left[ -\frac{1}{x} \right]_{1}^{2}\] \[=3\left[ -\frac{1}{2}+\frac{1}{1} \right]\] \[=3.\left( \frac{1}{2} \right)\] \[=\frac{3}{2}\]sq units