Question

1. Without evaluating the integral, show that \[ \left|\int_{C} \frac{d z}{z^{2}-1}\right| \leq \frac{\pi}{3} \] when \( C \) is the same arc as the one in Example 1, Sec. 43.

          1. Without evaluating the integral, show that
\[
\left|\int_{C} \frac{d z}{z^{2}-1}\right| \leq \frac{\pi}{3}
\]
when \( C \) is the same arc as the one in Example 1, Sec. 43.

1. Without evaluating the integral, show that

|∫C(d z)/(z^2-1)| ≤(π)/(3)

when C is the same arc as the one in Example 1, Sec. 43.

Added by Joel W.

Advanced Engineering Mathematics

Dennis G. Zill, Warren S. Wright 5th Edition

Chapter 18

Instant Answer

Solved by Expert Linda Winkler

Step 1

The contour \( C \) is an arc of the unit circle in the complex plane, typically parameterized by \( z = e^{i\theta} \) for \( \theta \) in some interval. Assume \( C \) is a semicircle or a similar arc. Show more…

Show all steps

Thanks for your feedback!

1. Without evaluating the integral, show that \[ \left|\int_{C} \frac{d z}{z^{2}-1}\right| \leq \frac{\pi}{3} \] when \( C \) is the same arc as the one in Example 1, Sec. 43.