 Hi friends I am Purva and today we will discuss the following question, find the area bounded by the curve y is equal to sin x between x is equal to 0 and x is equal to 2 pi. Now area 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 integral limit from a to b fx dx and this is the key idea which we will use to solve this question. Let us now begin with the solution. Now here we have to find the area of the region bounded by the curve y is equal to sin x between x is equal to 0 and x is equal to 2 pi. So first we shall draw the figure of y is equal to sin x between x is equal to 0 and x is equal to 2 pi. So now we draw a table and here we write x and here we write sin x. So when x is equal to 0 we have sin x is equal to 0, when x is equal to pi by 4 we have sin x is equal to 1 by root 2, when x is equal to pi by 2 we have sin x is equal to 1, when x is equal to 3 pi by 4 we have sin x is equal to 1 by root 2, when x is equal to pi we have sin x is equal to 0, when x is equal to 5 pi by 4 we have sin x is equal to minus 1 upon root 2, when x is equal to 3 pi by 2 we have sin x is equal to minus 1 and when x is equal to 2 pi we have sin x is equal to 0. So we have plotted these points on the graph and we have got this curve for y is equal to sin x between x is equal to 0 and x is equal to 2 pi and we have to find the area of this shaded region. Now since area is always taken as positive hence we take absolute value of the area below x axis. So we have hence the required area is equal to integral limit from 0 to pi sin x dx plus mod of integral limit from pi to 2 pi sin x dx and this is equal to now integrating sin x we get minus cos x and limit is from 0 to pi plus modulus plus integrating sin x again gives minus cos x and here we have limit is from pi to 2 pi. This is equal to now putting the limits we get minus cos pi minus minus cos 0 plus modulus of minus cos 2 pi minus minus cos pi this is equal to minus of now cos pi is equal to minus 1 now minus into minus becomes plus and cos 0 is equal to 1 plus modulus of minus cos 2 pi is equal to minus 1 minus into minus again becomes plus and we have cos pi is equal to minus 1 and this is equal to now minus into minus becomes plus so 1 plus 1 is equal to 2 plus modulus of minus 1 plus minus 1 gives minus 2 and this is equal to 2 plus modulus of minus 2 is 2 and this is equal to 4 hence we get the required area is equal to 4 so we write our answer as 4 hope you have understood the solution by and take care