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  4. The area bounded by the curve y=2 x4-x2, x-axis and the two ordinates corresponding to the minima of the function is

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Q. The area bounded by the curve $y=2 x^4-x^2, x$-axis and the two ordinates corresponding to the minima of the function is

Integrals

Solution:

$\frac{d y}{d x}=8 x^3-2 x, \frac{d y}{d x} =0 \Rightarrow \left(4 x^2-1\right) x=0$
image
$\Rightarrow x=-\frac{1}{2}, 0, \frac{1}{2}$
Required area $=-2 \int\limits_0^{1 / 2}\left(2 x^4-x^2\right) d x=\frac{7}{120}$