question_answer

The area of the region bounded by the curve \[y={{x}^{3}},\] and the lines, y= 8, and x = 0, is     JEE Main  Online Paper (Held On 19  May  2012)

A) 8                                             

B)                        12

C)                        10                                          

D)                        16

Correct Answer: B

Solution :

                Required Area \[=\int\limits_{y=0}^{8}{{{y}^{1/3}}dy}\] \[\left. =\frac{{{y}^{{}^{1}/{}_{3}+1}}}{\frac{1}{3}+1} \right|_{0}^{8}\left. =\frac{3}{4}\left( {{y}^{{}^{4}/{}_{3}}} \right) \right|_{0}^{8}\] \[=\frac{3}{4}\left[ {{(8)}^{{}^{4}/{}_{3}}}-0 \right]=\frac{3}{4}\left[ {{2}^{4}} \right]\] \[=\frac{3}{4}\times 16=12\]sq. unit.