question_answer

The area enclosed by \[y={{x}^{3}}\], its normal at \[(1,1)\]and x-axis is equal to

A) \[\frac{7}{4}\]                                   

B) \[\frac{9}{4}\]

C) \[\frac{5}{4}\]                                   

D)  2

Correct Answer: A

Solution :

Area\[=\int\limits_{0}^{1}{{{x}^{3}}}\,dx+\left( \frac{1}{2}\times 1\times 3 \right)=\frac{7}{4}\]