Question

Let f (x) be a continuous function given by f(x) = {(2x, |x| ≤ 1), (x² + ax + b, |x| > 1)

Find the area of the region in the third quadrant bounded by the curve x = -2y² and y = f(x) lying on the left of the line 8x + 1 = 0. 

Answer 1

Since f(x) is continuous (Fig.).

 

So, it must be continuous at x = 1, - 1, that is,

Now drawing the given curves.