How do I evaluate #int_(pi/2)^picscx dx#?
1 Answer
The answer is that this integral is DIVERGENT.
First of all I remember that:
Before integrate this function, it is useful to remember the parametric formula of sinus, that says:
Now the integral will be done with the method of substitution:
And it is important to change also the two limits of integrations:
if
if
It is clear that the integral becoms an improper integral. We can do the integral without the limits of integration and than we will do the final count.
Our integral becoms:
Now, using the fundamental theorem of Calculus, the final count:
So the integral is divergent.
Did we avoid ALL this counts? The answer is YES!
First of all a substitution:
If
if
The function