Answer:
2/5
Step-by-step explanation:
36 divided by 90 is 2/5.
When solving for X you do the opposite to a number if you are moving it to the other side of the problem. so, since x is being divided by 4/9, 4/9 would be multiplied to the opposite or to the 9/10.
Replace x with π/2 - x to get the equivalent integral
but the integrand is even, so this is really just
Substitute x = 1/2 arccot(u/2), which transforms the integral to
There are lots of ways to compute this. What I did was to consider the complex contour integral
where γ is a semicircle in the complex plane with its diameter joining (-R, 0) and (R, 0) on the real axis. A bound for the integral over the arc of the circle is estimated to be
which vanishes as R goes to ∞. Then by the residue theorem, we have in the limit
and it follows that
