 Hi and welcome to the session. I am Purva and I will help you with the following question. Find the area under the given curve and given line. y is equal to x square, x is equal to 1, x is equal to 2 and x axis. Now the area of the region enclosed by the curve y is equal to fx, x is equal to a, x is equal to b and x axis is given by integral limit is from a to b fx dx. So this is the formula to find the area of the region enclosed by some curve y is equal to fx where x is equal to a and x is equal to b that is x is from the limit is from a to b and x axis enclosed by x axis is given by integral limit from a to b fx dx. So this is the key idea which we will use to solve this question. Now we begin with the solution. Now we are required to find the area enclosed between y is equal to x square, x is equal to 1, x is equal to 2 and x axis. So let us first identify the region whose area is to be determined. Now y is equal to x square is a parabola with vertex at 0 0 and symmetric about y axis. So here we have drawn a parabola y is equal to x square with vertex at 0 0 and this is symmetric about y axis and x is equal to 1 and x is equal to 2 are the lines parallel to y axis and this parabola y is equal to x square cuts the line x is equal to 1 at the point 1 comma 1. Now this shaded region is the region whose area is to be found out. Therefore we have required area is equal to integral ordinate of the parabola dx and limit is from 1 to 2 and this is further equal to integral limit is from 1 to 2 ordinate of parabola which is x square dx and this further gives this is equal to now integral x square is equal to x cube by 3 and we have limit is from 1 to 2. Now putting the limits we get this is equal to upper limit that is 2 cube by 3 minus lower limit that is 1 cube by 3 and this is further equal to now 2 cube is equal to 8 by 3 minus 1 cube is equal to 1 by 3. This is equal to now 8 by 3 minus 1 by 3 gives 7 by 3 so we get our required area as 7 by 3. Hence the required area is equal to 7 by 3. This is our answer hope you have understood the solution take care and God bless you.