## 7.1. Riemann Integral

### Examples 7.1.13(a):

Since*| sin(x) | 1*we have:

for all-x x sin(x) x

*x*. By part 4 of the previous proposition we have:

for any- x dx x sin(x) dx x dx

*a, b*. But just as we computed

*x*in a previous exercise we could show that:

^{2}dx(which would be a nice and simple exercise). Putting everything together we get thatx dx = 1/2 (b^{2}- a^{2})

-8 x sin(x) dx 8