- #1

neom

- 13

- 0

**Decide if the following function is integrable on [-1, 1]**

[tex]f(x)=\left\{{sin(\frac1{x^2})\;\text{if}\;x\in[-1,\;0)\cup(0,\;1]\atop a\;\text{if}\;x=0}[/tex]

**where a is the grade, from 1 to 10, you want to give the lecturer in this course**

What I don't understand is how to find L(f, P) and U(f, P) since when I look at the graph of the function it oscillates a lot. So how do I choose the partition. It seems I would need an infinite partition almost to make it work. Or is there another way to do it?

Any help would be much appreciated as I am really lost on this problem.'

Edit: Sorry for the function not showing properly, don't know what I did wrong there

Should be

[tex]sin(\frac1{x^2})\;\text{if}\;x\in[-1,\;0)\cup(0,\;1][/tex]

&

[tex]a\;\text{if}\;x=0[/tex]