Calculate the path integral: $$\int_{\lambda}\left[2z + \sinh\left(z\right)\right]\,\mathrm{d}z$$

where $\displaystyle\lambda\left(t\right) = \frac{t^{2}}{4} + \frac{\mathrm{i}t}{2}\,,\quad \left(~0 ≤ t ≤ 4~\right)$.

Im not sure how to parameterize this and also how to answer the rest of the question so any help will be appreciated.

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    $\begingroup$ Can't you just find the anti-derivative ? $\endgroup$ – Zaid Alyafeai Mar 20 '17 at 21:54

Hint: Use the Fundamental Theorem of Calculus for contour integrals:

If $f$ is continuous on a domain $D$, then the integral along any path from $z_1$ to $z_2$ is given by $$ \int_{z_1}^{z_2} f(z) \, dz = F(z_2) - F(z_1) $$ where $F$ is any antiderivative of $f$.


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