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
<em>HOPE</em><em> </em><em>THIS</em><em> </em><em>WILL</em><em> </em><em>HELP</em><em> </em><em>U</em><em>.</em><em>.</em><em>.</em>
D is not a terminating decimal because it repeats *hint the dash mark above the 4*
![\sqrt[8]{48^4}](https://tex.z-dn.net/?f=%20%5Csqrt%5B8%5D%7B48%5E4%7D%20)
can be rewritten as
to the
power:
Now, applying exponent rules (multiply exponent inside parentheses by the one outside parentheses), we get:
This is equivalent to
, so now, we just simplify:
So:
![\sqrt[8]{48^4} =4 \sqrt{3}](https://tex.z-dn.net/?f=%20%5Csqrt%5B8%5D%7B48%5E4%7D%20%3D4%20%5Csqrt%7B3%7D)
Carissa value after x months=current+amount deposited
louan value after x months=current-amount taken out
carissa depositied=amount per month times x months=80x
louan take out=amount per month tiems x months=60x
when wil amount be equal
se equal
cariss=lousa
250+80x=1230-60x
add 60x both sides
250+140x=1230
minus 250 both sides
140x=980
divide both sides by 140
x=7
find how much that is
250+80(7)=250+560=810
7 months both have $810
