Is the Calculation of the Integral Along the Curve $\gamma(t)=1+it+t^2$ Correct?

[Dustinsfl]

$\gamma(t)=1+it+t^2, \ 0\leq t\leq 1$

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

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

 

[Chris L T521]

$\gamma(t)=1+it+t^2, \ 0\leq t\leq 1$

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

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

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

 

[Dustinsfl]

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

Yes