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The area in sq unit of the region A=\left \{ x,y:\left | x \right |+\left | y \right |\leq 1,2y^2\geq \left | x \right | \right \}
 
Option: 1 \frac{5}{6}
Option: 2 \frac{1}{6}
Option: 3 \frac{7}{6}  
Option: 4 \frac{1}{3}

Answers (1)

best_answer

Area of the shaded region

\\\text{Required area }= 4 \times \int_{0}^{1 / 2}\left((1-x)-\sqrt{\frac{x}{2}}\right) d x\\=4 \times\left[x-\frac{x^{2}}{2}-\frac{2}{3 \sqrt{2}} x^{3 / 2}\right]_{0}^{1 / 2}

\\=4 \times \left [\frac{1}{2}-\frac{1}{8}-\frac{2}{3 \sqrt{2} x} 2 \sqrt{2} \right ]\\ =4 \times \frac{5}{24}=\frac{5}{6}

Correct Answer : Option A

Posted by

himanshu.meshram

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