Step 1 Given- int_(0)^(pi)|cos x|dx To find- Evaluating the above integral using proper identities. Concept used- As the given integral is in modulus, so break the limit as per the given function. Step 2 Explanation- As the above integral in modulus, so using the property of modulus, proceeding as follows, Let, I=int_(0)^(pi)|cos x|dx Now, solving further, Splitting the function from 0 to (pi)/(2) and (pi)/(2) to pi and we know that cos x is postive for 0 to (pi)/(2) and negtaive for (pi)/(2) to pi . I=int_(0)^((pi)/(2))cos xdx-int_((pi)/(2))^(pi)cos x dx =[sin x]_(0)^((pi)/(2))-[sin x]_((pi)/(2))^(pi) =[sin (pi)/(2)-sin 0]-[sin pi -sin (pi)/(2)] =1-0-0+1 =2 Answer- The value of the integral int_(0)^(pi)|cos x|dx is 2.