The straight the through the origin which divides the area formed by the curves y = 2x $$-$$ x², y = 0 and x = 1 into two equal halves is

The area bounded by the parabolas $$y = 4{x^2},y = {{{x^2}} \over 9}$$ and the straight line y = 2 is

If $${x^2} + {y^2} = {a^2}$$, then $$\int\limits_0^a {\sqrt {1 + {{\left( {{{dy} \over {dx}}} \right)}^2}} dx = } $$

Area in the first quadrant between the ellipses x² + 2y² = a² and 2x² + y² = a² is