Question

If the area between the curve $y=2x^4-x^2$, the x-axis and the ordinates of two minima of the curve is $\frac{\lambda }{120}$ then find the value of $\lambda$.

• A. $5$
• B. $6$
• C. $7$
• D. $0$

Answer 1

The correct option is C $7$

$y=2x^4-x^2$
$y^{\prime }=8x^3-2x$
$y^{\prime }=0$
$x=0$ and $x=\pm \frac{1}{2}$
Checking sign of y'' to find out minima,
$y^{\prime \prime }=24x^2-2$
$y^{\prime \prime }\left(0\right)<0$ , maxima,
$y^{\prime \prime }(\pm 1/2).>0$ , minima
Limits $=\pm \frac{1}{2}$
Area bounded $=\int ydx$
$={\int }_{-1/2}^{1/2}(2x^4-x^2)dx$
$=\frac{7}{120}$