MathCS.org - Real Analysis: Examples 7.1.13(a):

Examples 7.1.13(a):

Find an upper and lower estimate for x sin(x) dx over the interval [0, 4].

Back

Since | sin(x) | 1 we have:

-x x sin(x) x

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

- x dx x sin(x) dx x dx

for 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

Next | Previous | Glossary | Map | Discussion