Find the area bounded by the curve y = √x,x = 2y+3 in the first quadrant and x-axis.

Find the area bounded by the curve y = √xx = 2y+3 in the first quadrant and x-axis.

We have y = √x and x = 2y+2,Solving we get ,y = √2y+3, y≥0,⇒ y,2, = 2y+3,y≥0,⇒ y,2, - 2y - 3 = 0, y≥0,⇒ (y-3)(y+1) = 0, y≥0,⇒ y = 3,The graph of function y = √x is part of parabola y2 = x lying bove x-axis.,The graph is as shown in the following figure.