question_answer

The area in sq unit enclosed by the curve\[y=4{{x}^{3}}\]the\[x-\]axis and the lines\[x=6\]and\[x=9\]is:

A)  2 sq unit             

B)  1 sq unit                             

C)  4 sq unit       

D)         3 sq unit

E)  6 sq unit

Correct Answer: D

Solution :

Required area\[=\int_{6}^{9}{\frac{36}{{{x}^{2}}}}dx=\left[ -\frac{36}{x} \right]_{6}^{9}\] \[=-36\left[ \frac{1}{9}-\frac{1}{6} \right]=3\,sq.\,unit\]