 Hello and welcome to the session. I am Deepika here. Let's just answer the question which says the area between X is equal to Y square and X is equal to 4 is divided into two equal parts by the line X is equal to 8. Find the value of A. Now we know that the area A of the region bounded by the curve Y is equal to Fx x-axis and the lines X is equal to A and X is equal to B is given by area is equal to integral from A to B Y dx which is 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 We will draw the figure to identify the area between the given curve X is equal to Y square and X is equal to 4 now X is equal to Y square or Y square is equal to X is a parabola with vertex at the origin and symmetrical about X-axis Where X is equal to 4 is a line parallel to Y-axis Therefore according to our key idea area is equal to twice integral from 0 to 4 Y dx by taking vertical strips because we can think area of the shaded region in the first quadrant as composed of large number of very thin vertical strips of height Y and width dx So the total area of the shaded region in the first quadrant is equal to integral from 0 to 4 Y dx Now we have Y square is equal to X this implies Y is equal to plus minus under root of X We consider only the numerical value of the area Therefore area is equal to twice integral from 0 to 4 under root of X dx and this is equal to 2 into X raised to power 3 by 2 over 3 by 2 from 0 to 4 and This is again equal to 2 into 2 over 3 into 4 raised to power 3 by 2 minus 0 raised to power 3 by 2 which is 0 So this is equal to 4 over 3 Into now 4 can be written as 2 raised to power 2 Now 4 raised to power 3 by 2 is 2 raised to power 2 into 3 by 2 and this is equal to 4 over 3 Into 2 Q which is 8 so this is equal to 32 over 3 So area of the shaded region is 32 over 3 now X is equal to a divides this area Into 2 equal parts therefore twice integral from 0 to a Y dx is equal to 16 over 3 or twice integral from 0 to a Under root of X dx is equal to 16 over 3 or twice Into X raised to power 3 by 2 over 3 by 2 from 0 to a is equal to 16 over 3 or 2 over 3 Into a raised to power 3 by 2 minus 0 raised to power 3 by 2 is 0 is equal to 16 over 3 or 4 over 3 Into a raised to power 3 by 2 is equal to 16 over 3 a raised to power 3 by 2 is equal to 16 over 3 into 3 over 4 or A is equal to It's to power 2 over 3 hence the value of a is 4 raised to power 2 over 3 and this is our answer. I Hope the solution is clear to you. Bye and take care