Find the area bounded by the curve y = 2x - x2 and the straight line y = -x.
Answer & explanation
Correct answer: option 3
y = 2x -x2 is (x - 1)2 = -(y - 1)
It represents a parabola with vertex at (1, 1).
$A=|\int_0^3(y_1-y_2)dx|$
$=|\int_0^3(2x^2-x^2)+x\,dx|=|(\frac{3x^2}{2}-x^3)|=\frac{9}{2}$