Q. Area of the region bounded by the curve $y^2 = 4x$ , y-axis and the line y = 3 is.
Application of Integrals
Solution:
The curve $y^2 = 4x$ is the parabola MP is the line y = 3.The area of the region bounded by $y^2 = 4x$, and y = 3 is
$A = \int^{3}_{0} x dy = \int^{3}_{0} \frac{y^{2}}{4} dy = \left[\frac{y^{3}}{12}\right]_{0}^{3} = \frac{27}{12} = \frac{9}{4} $
