Examples 7.1.13(a):
Since | sin(x) | 1 we have:-x x sin(x) xfor all x. By part 4 of the previous proposition we have:
- x dx x sin(x) dx x dxfor any a, b. But just as we computed x2 dx in a previous exercise we could show that:
x dx = 1/2 (b2 - a2)(which would be a nice and simple exercise). Putting everything together we get that
-8 x sin(x) dx 8