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[SOLVED] primitive

dwsmith

Well-known member
Feb 1, 2012
1,673
How can I find the primitive of $\int_{\gamma}ze^{z^2}dz$ from $i$ to $2-i$?
 

Ackbach

Indicium Physicus
Staff member
Jan 26, 2012
4,189
How can I find the primitive of $\int_{\gamma}ze^{z^2}dz$ from $i$ to $2-i$?
$$\int z e^{z^{2}}\,dz=\frac{1}{2}\int 2z e^{z^{2}}\,dz.$$

Can you finish?
 

dwsmith

Well-known member
Feb 1, 2012
1,673
$$\int z e^{z^{2}}\,dz=\frac{1}{2}\int 2z e^{z^{2}}\,dz.$$

Can you finish?
So $\left(\frac{e^{z^2}}{2}\right)'=\int ze^{z^2}dz$ Then to solve the integral I just integrate g'(z) right?
 

Ackbach

Indicium Physicus
Staff member
Jan 26, 2012
4,189
So $\left(\frac{e^{z^2}}{2}\right)'=\int ze^{z^2}dz$ Then to solve the integral I just integrate g'(z) right?
Actually, I would have said that

$$\left(\frac{e^{z^{2}}}{2}\right)'=ze^{z^{2}}.$$

Then just use the Fundamenal Theorem of the Calculus, which works because your function is analytic.