Find the area bounded by $y^2=x^2(1-x^2)$? I think in this way as the graph lies between -1 to 1 the area is 4 times of $\int x \sqrt{1-x^2} dx$ limits from 0 to 1. Am I correct?
2026-03-30 00:04:48.1774829088
Area bounded by$ y^2=x^2(1-x^2)$
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Yes, the area enclosed by such a lemniscate is: $$ 4\int_{0}^{1}x\sqrt{1-x^2}\,dx = 4\int_{0}^{\pi/2}\sin(\theta)\cos^2(\theta)\,d\theta = \color{red}{\frac{4}{3}}.$$