Find the area bounded by the curve y = 2x - x2 and the straight line y = -x.

$\frac{1}{2}$ $\frac{3}{2}$ $\frac{9}{2}$ None of these

$\frac{9}{2}$

y = 2x -x2 is (x - 1)2 = -(y - 1) It represents a parabola with vertex at (1, 1). $A=|\int_0^3(y_1-y_2)dx|$ $=|\int_0^3(2x^2-x^2)+x\,dx|=|(\frac{3x^2}{2}-x^3)|=\frac{9}{2}$