 Hi, and welcome to our session. Let us discuss the following question. The question says evaluate the following integral of mod x minus 1 from 0 to 4. Let's now begin with this illusion. Let i is equal to integral of mod x minus 1 from 0 to 4. mod of x minus 1, this is equal to minus of x minus 1 if x is less than 1. And this is equal to x minus 1 if x is greater than 1. We know that integral of fx from a to b is equal to integral of fx from a to c plus integral of fx from c to b where c lies between a and b. Now using this property integral of mod x minus 1 from 0 to 4 is equal to integral of minus of x minus 1 from 0 to 1. Now here a is equal to 0, c is equal to 1, and b is equal to 4. Plus integral of x minus 1 from 1 to 4. This is equal to integral of minus x from 0 to 1 plus integral of 1 from 0 to 1 plus integral of x from 1 to 4 minus integral of 1 from 1 to 4. We know that integral of xn with respect to x is equal to x to the power n plus 1 by n plus 1. Now using this formula integral of x is x square by 2 and we have minus sign with it. So this is equal to minus x square by 2 where the lower limit is 0 and upper limit is 1 plus integral of 1 with respect to x is x where the lower limit is 0 and upper limit is 1 plus integral of x with respect to x is x square by 2 where the lower limit is 1 and upper limit is 4 minus integral of 1 with respect to x is x where the lower limit is 1 and upper limit is 4. Now by using second fundamental theorem of integral calculus we get minus into 1 square by 2 minus 0 square by 2 plus 1 minus 0 plus 4 square by 2 minus 1 square by 2 minus 4 minus 1. This is equal to minus 1 by 2 plus 1 plus 16 by 2 minus 1 by 2 minus 3. This is equal to 1 by 2 plus 15 by 2 minus 3. This is equal to 1 plus 15 minus 6 by 2. This is equal to 10 by 2 and this is equal to 5. Hence the required answer is 5. So this completes the section. Bye and take care.