Author Topic: TUT5101 QUIZ3  (Read 945 times)

Yiheng Bian

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TUT5101 QUIZ3
« on: February 06, 2020, 12:34:14 AM »
$$
\int_{\Upsilon}e^z dz
$$
$$
\text{line from 0 to } z_{0}$$
Therefore
$$
r(t)= tz_{0}
$$
$$
r'(t) = z_{0} (0\leq t \leq 1)
$$
And since
$$
f(z)=e^z
$$
$$
f(r(t))= e^{z_{0}}
$$
So
$$
\int_{\Upsilon}e^z dz =  \int_{0}^{1}f(r(t))r'(t)dt = \int_{0}^{1}e^{tz_{0}}z_{0} dt = z_{0}(\frac{1}{z_{0}}e^{z_{0}}- \frac{1}{z_{0}})= e^{z_{0}} - 1
$$
« Last Edit: February 09, 2020, 07:36:30 PM by Yiheng Bian »