 Hello and welcome to the session on the Pica here. Let's discuss the question it says find the area of the region bounded by the curve y square is equal to 4x and the line x is equal to 3. Now we know that the area A of the region bounded by the curve y is equal to fx, x is equal to A and x is equal to B is given by A is equal to integral from A to B y dx and this is again equal to integral from A to B f of x dx. So this is a key idea behind our question. We will take the help of this key idea to solve the above question. So let's start the solution. Find the region whose area we have to find is equal to 4x is a parabola with what is at the origin and symmetrical about is a line parallel to y So the given curve represented by the equation clear is equal to 4x is a parabola with what is the origin symmetrical about x axis. We have to find the area of this shaded region and the shaded region is bounded by the curve y square is equal to 4x, x is equal to 0 and x is equal to 3 and is symmetrical about therefore the area of the shaded region is equal to 2 into area of the shaded region in the first quadrant by taking vertical strips of height y and width dx the area of the shaded region in the first quadrant is integral from 0 to 3 y dx therefore the total area of the shaded region A is equal to twice integral from 0 to 3 y dx now we have y square is equal to 4x this implies y is equal to plus minus 2 under root of x therefore area is equal to twice integral from 0 to 3 now we will consider only the positive sign as we have to consider the area in the first quadrant so this is equal to 4 into 3 is to power 3 by 2 over 3 by 2 limits are from 0 to 3 and this is equal to 4 into 2 over 3 into 3 is to power 3 by 2 minus 0 is to power 3 by 2 which is 0 and this is equal to 8 over 3 into 3 is to power 3 by 2 and this is again equal to 8 into 3 is to power 3 by 2 minus 1 and this is again equal to 8 into 3 is to power 1 by 2 and this is equal to 8 under root of 3 hence the required area is 8 under root of 3 so the answer for the above question is 8 under root of 3 I hope the solution is clear to you bye and take care