The area between the curve `y=2x^(4)-x^(2)`, the x-axis, and the ordinates of the two minima of the curve is

Options

A. `(7)/(120)` sq unit
B. `(9)/(120)` sq unit
C. `(11)/(120)` sq unit
D. `(13)/(120)` sq unit

Answer

A

Explanation

`becausey=2x^(4)-x^(2)therefore(dy)/(dx)=8x^(3)-2x`
For maxima or minima, put `(dy)/(dx)=0`, we get `x=-(1)/(2),0,(1)/(2)`
Then, `((d^(2)y)/(dx^(2)))_(x=(1)/(2))gt0,((d^(2)y)/(dx^(2)))_(x=(-1)/(2))gt0,((d^(2)y)/(dx^(2)))_(x=0)lt0`
`therefore` Required area `=|int_(-1//2)^(1//2)(2x^(4)-x^(2))dx|=|[(2x^(5))/(5)-(x^(3))/(3)]_(-1//2)^(1//2)|`
`=|(2)/(5).(1)/(32)-(1)/(24)+(2)/(5).(1)/(32)-(1)/(24)|=(7)/(120)` sq unit