Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

How to find this integral?

$$\int_c (x^2+iy^3)dz$$ when

$c$ is a segment that connects $z=1$ with $z=i$?

I know that $z(t) = (1-t)z_1 + tz_2 = 1 -t+ti$.

How do I use that in this cases?

share|cite|improve this question

1 Answer 1

up vote 1 down vote accepted

$$\int_c (x^2+iy^3) dz = \int_0^1 \left[(1-t)^2+i(t)^3\right]z'(t)dt $$

because $x=1-t$ and $y=t$ per what you've written, and $z'(t)=i-1$. Now if you take the scalar factor of $z'$ outside the integral you can evaluate it with real calculus and then multiply to finish.

share|cite|improve this answer
I've now realized that the book I am reading is a tragedy. I couldn't figure this out by myself. – tamakisnen Jan 26 '12 at 20:51

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.