 Hello and welcome to the session. I am Deepika here. Let's discuss a question which says, evaluate the following definite integral integral from pi by 6 to pi by 4 cos x dx. Now we know that by second fundamental theorem of integral calculus a to b fx dx where fb continuous function defined on the closed interval a b is equal to derivative and this is again equal to that is the integral of a to b fx derivative at the lower limit a. So I help up this key idea to solve the above questions. So let's start the solution. This is equal to definite integral of cos x dx law of mod x minus 4t that is the empty derivative of 4 by second fundamental theorem equal to pi by 4 this is equal to law of pi by 4 minus 4t pi by 4 minus law cos x pi by 6 minus 4t pi by 6 and this is equal to law now cos x pi by 4 is root 2 minus 4t pi by 4 is 1 minus law cos x pi by 6 is 2 minus 4t pi by 6 is root 3 now log m minus log m is equal to log m over n log of root 2 minus 1 upon 2 minus root 3 the answer for the above question is law of this 1 upon minus root 3 I hope the solution is clear to you bye and take care