the value of a and b is not given. I don't understand how to prove.
Here is a hint. How would you do it for one point?
i.e let $\displaystyle c \in (a,b)$
$\displaystyle f(x)=\begin{cases} 0, x \ne c \\ M, x=c \end{cases}$
$\displaystyle \int_{a}^{b}f(x)dx$
Let P be the partition $\displaystyle \{a,c-\frac{\epsilon}{2|M|},c+\frac{\epsilon}{2|M|},b\}$
Now how would you do it for 2,3 or any finite number?
I hope this helps.
I understand the strategy. The textbook gives 2 hints. It says to use theorem 3.1.2 and to use the solution of the previous problem. Unfortunately, I have not been able to find the solution of previous problem. I posted the previous problem at
http://www.mathhelpforum.com/math-he...ntegrable.html
but no one gave any idea. If I get an idea out of the previous problem, I can solve this problem because it appears to be related.
Partition of [a, b] will be (b-a) / n where n is the number of increments. So the partition will look like
{a, a + (b-a)/n , a + (b-a)/n + (b-a)/n, ......b}