How do you find the definite integral of #tan x dx# from #[pi/4, pi]#?
1 Answer
Actual Value: Impossible to determine
Value by Cauchy's Principal Value:
Explanation:
For a simple answer, this integral doesn't converge (it has an asymptote at
However, if we use Cauchy principal value, we can derive the above answer.
We are asked to find
Recall that
This is currently very hard to integrate. Let's attempt a u-substitution.
Let
By the rule
Evaluate using the second fundamental theorem of calculus, which states that
Hopefully this helps!