Toronto Math Forum
MAT3342020F => MAT334Lectures & Home Assignments => Chapter 1 => Topic started by: Nathan on October 06, 2020, 06:08:35 PM

Question: $\int_y Re(z) dz$ where $y$ is the line segment from 1 to $i$.
I can't get the same answer as the one in the textbook.
Answer in textbook: $\frac{1}{2}(i1)$
My answer:
$y(t)=$
$= 1 + (i  1)t$
$= (1  t) + it$
$y'(t) = i  1$
$\int_y Re(z) dz=$
=$\int_1^i (1t)(i1)dt$
$=\int_1^i i  1  ti + t dt$
$=ti  t  \frac{t^2i}{2} + \frac{t^2}{2}^i_1$
$=1 i + \frac{i}{2}  \frac{1}{2}  (i  1\frac{i}{2} + \frac{1}{2})$
$=i  1$
What is wrong with my answer?

Hi Nathan.
The mistake seems to be in your bounds of integration, not the process itself. With the way you parameterized the line, the integral should be from 0 to 1, not 0 to i.