 Hello and welcome to the session. In this session we discussed the following question which says evaluate the following integral, integral 0 to pi modulus cos x dx. Let's see its solution. We first assume let i be equal to the integral 0 to pi modulus cos x dx. Now first let's define modulus cos x. This is equal to cos x if cos x is greater than equal to 0 and this is equal to minus cos x if cos x is less than equal to 0 or you can say modulus cos x is equal to cos x if x is greater than equal to 0 less than equal to pi by 2 and this is equal to minus cos x if x is greater than equal to pi by 2 less than equal to pi. So now i that is equal to integral 0 to pi modulus cos x dx can be written as integral 0 to pi by 2 modulus cos x dx plus integral pi by 2 to pi modulus cos x dx. Now when x is between 0 and pi by 2 then modulus cos x is equal to cos x. So we have i is equal to integral 0 to pi by 2 cos x dx plus now when x is between pi by 2 and pi then modulus cos x is equal to minus cos x. So this could be written as integral pi by 2 to pi minus cos x dx. From here we have i is equal to integral 0 to pi by 2 cos x dx minus integral pi by 2 to pi cos x dx. This gives us i equal to now integral of cos x dx is sin x. So sin x and the limit goes from 0 to pi by 2 minus sin x and limit goes from pi by 2 to pi. That is i is equal to sin pi by 2 minus sin 0 minus sin pi minus sin pi by 2 that is we get i is equal to the sin pi by 2 is 1 minus sin 0 which is 0 minus sin pi is 0 minus sin pi by 2 is 1. So this is equal to 1 plus 1 equal to 2. So we have i is equal to 2 that is we say integral 0 to pi modulus cos x dx is equal to 2. So this is our final answer. This completes the session. Hope you have understood the solution for this question.