The area in square unit enclosed by the curve $x^2 y=36$, the $x$-axis and the lines $x=6$ and $x=9$ is

• A

  2 sq unit
• B

  1 sq unit
• C

  4 sq unit
• Correct answer
  D

  3 sq unit

Solution

$\begin{aligned} \text { Required area } & =\int_6^9 \frac{36}{x^2} d x=\left[-\frac{36}{x}\right]_6^9 \\ & =-36\left[\frac{1}{9}-\frac{1}{6}\right]=3 \text { sq unit }\end{aligned}$

Hence, the correct answer is option: 'D'.