Homework Sourseintegrate secx2 tanx2 dx where a0 and bpi2Solution Since th
integrate sec(x/2) * tan(x/2) dx where a=0 and b=pi/2
Solution
Since there is an infinite discontinunity at x = p/2, re-write the integral as follows: ? sec(x) dx (from x=p/2 to p) = lim (n-->p/2+) ? sec(x) dx (from x=n to p). Integrating now yields: lim (n-->p/2+) ? sec(x) dx (from x=n to p) = lim (n-->p/2+) [ln|tan(x) + sec(x)| (evaluated from x=n to p)] = lim (n-->p/2+) [0 - ln|tan(n) + sec(n)] = -infinity. Therefore, the integral is divergent.
