Question

The area of the region in the xy-plane defined by the inequalities $x-2y^2\ge 0,1-x-\left|y\right|\ge 0$ is

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{1}{4}$
• D. $\frac{7}{12}$

Answer 1

The correct option is D $\frac{7}{12}$

Area = $2{\int }_0^{\frac{1}{2}}\sqrt{\frac{x}{2}}dx+\frac{1}{4}=\frac{7}{12}$