Guys!

I'm deriving something that I feel is cool, and I am so close to the answer, but i'm getting both the positive as well as a negative value as an answer. I need some solid proof to reject one of the answers as the internet only gives the positive value as an answer...Help?

The question is : $\int _{ 0 }^{ \infty }{ \sin { ({ x }^{ 2 }) } dx }$
And I have solved it like this:

#Integration #Complex

Easy Math Editor

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Comments

Just looking at the graph, you know that the answer has to be positive. I will look at your work later...

Otto Bretscher - 5 years, 8 months ago

@Otto Bretscher I thought so too, but by looking at the graph, we can say that the first positive area is large...But if the limit continues upto infinity, we can't say that the total sum is positive, can we?