question_answer

The area bounded by the curve \[y={{x}^{3}},\] \[x-\]axis and two ordinates \[x=1\] to \[x=2\] equal to                [MP PET 1999]

A)            \[\frac{15}{2}\] sq. unit   

B)            \[\frac{15}{4}\] sq. unit

C)            \[\frac{17}{2}\] sq. unit   

D)            \[\frac{17}{4}\] sq. unit

Correct Answer: B

Solution :

                   Shaded area \[=\int_{1}^{2}{y\,dx}\]\[=\int_{1}^{2}{{{x}^{3}}.dx=\frac{1}{4}[{{x}^{4}}]_{1}^{2}}\]                    \[A=\frac{1}{4}[16-1]=\frac{15}{4}\] sq. unit.