+0

# why it is diverge

0
515
3
+1832

I think it must be 1 converge

because the term that I circled it equal to zero !

I'm I right ?

Mar 17, 2015

#3
+27549
+10

and Wolfram Alpha won't evaluate it.

.

Mar 18, 2015

#1
+99352
+5

Here is the graph.

https://www.desmos.com/calculator/orgvwef1o3

Why does what you circled =0 ??

What does diverge and converge mean?

Thinking about what they 'may' mean this doesn't really do either does it?

I know I am out of my depth here.

I guess I am hoping someone will teach me something that is easy to learn. (Well one can dream)  :)

Mar 18, 2015
#2
+98173
+10

Like Melody, I'm on shaky ground here....so.....you might have to take this with a grain of salt....

By the Integral Test, the function in the integrand must be eventually positive and decreasing on the interval of interest - in this case, 0 to ∞.

Here's the graph of  y = cos(x)*e^(-sin(x))

Note that this function is not eventually positive and decreasing on the interval (it is periodic).....thus.....the integral diverges

That's my two cents worth.....

Alan???  heureka???....to the rescue???

Mar 18, 2015
#3
+27549
+10