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[SOLVED] Simply complex integral

dwsmith

Well-known member
Feb 1, 2012
1,673
$\gamma(t)=1+it+t^2, \ 0\leq t\leq 1$

$\displaystyle\int_0^1 (1+it+t^2)(i+2t)dt=\int_0^1(2t^3+t)dt+i\int_0^1(1+3t^2)dt = 1 + 2i$

I was told that was wrong. What is wrong with it?
 

Chris L T521

Well-known member
Staff member
Jan 26, 2012
995
$\gamma(t)=1+it+t^2, \ 0\leq t\leq 1$

$\displaystyle\int_0^1 (1+it+t^2)(i+2t)dt=\int_0^1(2t^3+t)dt+i\int_0^1(1+3t^2)dt = 1 + 2i$

I was told that was wrong. What is wrong with it?
What was the original problem? To solve $\displaystyle \int_{\gamma} z\,dz$ where $\gamma(t) = 1+it+t^2$, $t\in [0,1]$??
 

dwsmith

Well-known member
Feb 1, 2012
1,673