The area of the region enclosed between the parabolas y 2 = 2 x - 1 and y 2 = 4 x - 3 is.

Step-by-step solution

We have, y 2 = 2 x - 1       . . . 1 and y 2 = 4 x - 3       . . . 2 We first find the points of intersection of the given parabolas by solving the equations 1   &   2 simultaneously. This gives, 2 x - 1 = 4   x - 3 ⇒    2 x = 2 ⇒ x = 1 Now, put x = 1 in equation 1 , we get y = ± 1 . Now, the equations 1   &   2 can be written as y 2 = 2 x - 1 2 y 2 = 4 x - 3 4 respectively. The graphs of these two curves are shown in figure.