Question

5. Find the integral $ \int_\gamma ze^{z^2} dz $ (a) from the point i to the point -i + 2, taken along a straight line segment, and (b) from 0 to 1 + i along the parabola y = x².

          5. Find the integral \( \int_\gamma ze^{z^2} dz \)
(a) from the point i to the point -i + 2, taken along a straight line segment, and
(b) from 0 to 1 + i along the parabola y = x².

5. Find the integral ∫γ ze^z^2 dz
(a) from the point i to the point -i + 2, taken along a straight line segment, and
(b) from 0 to 1 + i along the parabola y = x².

Added by Jessica W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Mengchun Cai

01/31/2024

Step 1

Then $F(z) = \frac{1}{2}e^{z^2}$ is an antiderivative of $f(z)$ since $F'(z) = \frac{1}{2} \cdot 2z e^{z^2} = ze^{z^2} = f(z)$. By the fundamental theorem of calculus for line integrals, $\int_\gamma ze^{z^2} dz = F(z_1) - F(z_0)$, where $z_0$ and $z_1$ are the Show more…

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5. Find the integral $\int_\gamma ze^{z^2} dz$ (a) from the point $i$ to the point $-i + 2$, taken along a straight line segment, and (b) from 0 to $1 + i$ along the parabola $y = x^2$.