 Hi and welcome to the session. Let's work out the following question. The question says, find the area enclosed by the parabola y squared equal to x and the line y plus x equal to 2. Let's start with a solution to this question. We see that the given parabola is y squared equal to x and the line is y plus x equal to 2. First of all, we will find the points of intersection of the parabola and the line. So, we put y equal to 2 minus x. We call this equation 1 and this equation 2. So, we put y equal to 2 minus x in the first equation. This gives us 2 minus x, the whole square is equal to x. This implies 4 plus x squared minus 4x is equal to x. This implies 4 minus 4x minus x plus x squared is equal to 0. This implies x squared minus 5x plus 4 is equal to 0. This implies x squared minus 4x minus x plus 4 is equal to 0. This further implies that x into x minus 4 minus 1 into x minus 4 is equal to 0. So, this implies x minus 1 into x minus 4 is equal to 0. This means that either x is equal to 1 or x is equal to 4. Now, when x is equal to 1 then y plus 1 is equal to 2 implies that y is equal to 1. Now, when x is equal to 4 and y plus 4 is equal to 2 implies y is equal to minus 2. So, the two points of intersection of the parabola and the line are 1, 1 and 4 minus 2. So, let us draw the line and the graph sorry line and the parabola on the graph. These are the two points of intersections. Therefore, we can say that the required area is this shaded portion that is equal to integral where limit goes from minus 2 to 1 such that y plus x is equal to 2 that is the line minus integral where limit goes from minus 2 to 1 x where y square is equal to x. Now, this is dy this is also dy. This is equal to integral where limit goes from minus 2 to 1 this will be 2 minus y dy minus integral where limit goes from minus 2 to 1 y square dy this is equal to integral where limit goes from minus 2 to 1 2 minus y minus y square dy this is equal to 2y minus y square by 2 minus y cube by 3 where limit goes from minus 2 to 1 this is equal to 2 minus 1 by 2 minus 1 by 3 minus 2 into minus 2 minus minus 2 the whole square divided by 2 minus minus 2 the whole cube divided by 3 this is equal to 2 minus 1 by 2 minus 1 by 3 minus minus 4 minus 2 plus 8 by 3 this is equal to 2 minus 1 by 2 minus 1 by 3 minus minus 6 plus 8 by 3 this is equal to 2 minus 1 by 2 minus 1 by 3 plus 6 minus 8 by 3 this is equal to 8 minus 1 by 2 minus 1 by 3 minus 8 by 3 and that is equal to 9 by 2 square units this is our answer to this question I hope that you understood the solution and enjoyed the session have a good day