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  4. The area bounded by the curve 2x2 + y2 = 2 is

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Q. The area bounded by the curve $2x^{2} + y^{2} = 2$ is

Application of Integrals

Solution:

Area bounded by the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$
between limits $x = a$ to $x = b$ is $\pi ab$
Here, $a = 1$, $b =\sqrt{2}$
Required area $=\pi\sqrt{2}$ sq. units.