# estimation

• May 5th 2009, 09:15 AM
Abbas
estimation
I got stucked with this problem !
any rule or thereom to slove it

Find bounds m and M such that $m \le x\sin(x) \le M$
use the to estimate $\int_{0}^{\pi}x\sin(x)dx$
• May 5th 2009, 02:17 PM
Spec
If $f(x_1) \leq f(x) \leq f(x_2)$, then $f(x_1)(b-a) \leq \int_a^b f(x) dx \leq f(x_2)(b-a)$

So if you know the boundaries of $m \leq x\sin x \leq M$ on $x \in [0,\pi]$, then you can also estimate the integral with $m(\pi-0) \leq \int_0^\pi x \sin x dx \leq M(\pi-0)$