 Hi and welcome to the session. I am Purva and I will help you with the following question. Proof the following. Integral limit is from minus 1 to 1, x raised to the power 17 into cos raised to the power 4x dx is equal to 0. Now suppose we have a definite integral fx dx where limit is from minus a to a. Then if this f is an odd function that is if f is an odd function then we have this definite integral is equal to 0. So this is the key idea which we will use in this question. Now we pick in with the solution. We denote this left hand side by i. So we have i is equal to integral limit is from minus 1 to 1, x raised to the power 17 into cos raised to the power 4x dx. Now if we take x raised to the power 17 into cos raised to the power 4x as 1 function say f then we know that an odd function into an even function is equal to an odd function. So we get f is an odd function here and also we have the limit is from minus 1 to 1. So by key idea we can straight away say that this is equal to 0 because here we have limit from minus a to a and f is an odd function. So we get i is equal to 0. Thus we get integral limit is from minus 1 to 1, x raised to the power 17 into cos raised to the power 4x dx is equal to 0. Hope you have understood the solution. Take care and have a nice day.