How do I solve for k in an equation with integrals?
#\int_0^k \frac{sec^2(x)}{1 + tan(x)} = ln(2)#
I need to solve the above equation for k. This is what I did:
#[ln|1+tan(x)|]_0^k = ln(2)#
#ln|1 + tan(k)| - ln|1 + tan(0)| = ln(2)#
#ln|1 + tan(k)| = ln(2)#
#|1 + tan(k)| = 2#
#1 + tan(k) =+-2 #
#tan(k) = -1+-2#
This gives us:
# k = pi/4 + npi# where n is any integer
and
#k = tan^-1(-3) + npi# where n is any integer
My problem is that the only value of k that actually works in the original equation is # k = pi/4# .
Why do the other ones not work (for example #k = (5pi)/4# )?
I need to solve the above equation for k. This is what I did:
This gives us:
and
My problem is that the only value of k that actually works in the original equation is
Why do the other ones not work (for example
1 Answer
Aug 15, 2017
If you try to integrate past an asymptote, the integral does not converge.
Explanation:
The integrand is not defined where
And the improper integral past such a point does not converge.
