Integrals are not always easy to evaluate; sometimes we need to be clever! In this problem we study the definite integral x sin(x) 1 = dx. 1 + cos2(x) At first, it appears difficult to evaluate this integral with substitution (you can try with simple substitution ideas...). But it can be done! Let's see how it goes. (a) Use the substitution u = 7 - x to show that sin(x) 1 = dx. 2 1 + cos2(x) (Recall that sin(n - x) = sin(x) and cos(n - x) = - cos(x).) (b) Evaluate the remaining definite integral using substitution to get: I = 4