Please help me answer the following questions!

Q1: Q2: Preview Preview Find the line y = mx through the origin, with positive slope, which together with the parabola y = x2 encloses a region of area . Integrals are not always easy to evaluate; sometimes we need to be clever! In this problem we study the definite integral Q3: x sin(x) dx. 1 + cos2(x) Preview The n-th harmonic number is defined by 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 1 + +... + it goes n (a) Use the substitution u = it - x to show that Show that sin(x) 1 - x dx. H,, = 2 1 + cos(x) 1 -x dx. (Recall that sin(7 - x) - sin(x) and cos(7 - x - - cos(x)) (b) Evaluate the remaining definite integral using substitution to get: 14