 Hi and welcome to the session. Let's work out the following question. The question says find the area of the region bounded by the curve y equals to x square and the line y equals to x. So let's start with the solution to this question. The given curve is y equals to x square and the line y equals to x. Now putting y equal to x in this one we get x is equal to x square. This implies that x is equal to 1. If x is equal to 1 so by this we can say that y is also equal to 1. Therefore the point of intersection of the parabola y equals to x square and the line y equals to x is 1 1. So this is how we draw the figure. This is the parabola y equals to x square. This is the line y equals to x. So this is the required area, the shaded area. Therefore the required area is equal to the integral where limit goes from 0 to 1 that is from this point that is 0 to this point that is 1 on x axis of y such that y is equal to x we can say y as in for the line y equals to x dx minus integral where limit goes from 0 to 1 y where y is equal to x square dx that is equal to integral where limit goes from 0 to 1 x minus x square dx which is further equal to x square by 2 minus x cube by 3 where limit goes from 0 to 1. This is equal to 1 by 2 minus 1 by 3 that is equal to 1 upon 6 square units. So this is our answer to this question. I hope that you understood the solution and enjoyed the session. Have a good day.