The area between the curve `y=2x^4-x^2,` the axis, and the ordinates of the two minima of the curve is 11/60 sq. units (b) 7/120 sq. units 1/30 sq. units (d) 7/90 sq. units

Options

A. `11//60` sq. units
B. `7//120` sq. units
C. `1//30` sq. units
D. `7//90` sq. units

Answer

B

Explanation

The curve is `y=2x^(4)-x^(2)=x^(2)(2x^(2)-1)`
The curve is symmetrical about the axis of y.
Also, it is a polynomial of 4 degree having roots `0,0,pm(1)/(sqrt(2)).x=0` is a repeated root. Hence graph touches at (0,0).
The curve intersects the axes at `O(0,0), A(-1//sqrt(2),0) and B(1//sqrt(2),0).`
Thus, the graph of the curve is as shown in the figure.

Here, `yle0`, as x varies from `x=-1//2" to "x=1//2`
`therefore" required area =2 Area "OCDO`
`=2|int_(0)^(1//2)ydx|`
`=2|int_(0)^(1//2)(2x^(4)-x^(2))dx|`
`=7//120` sq. units