Answered: Evaluate the given integral where C is…

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Evaluate the given integral where C is the left half of the unit circle in ccd.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.3: The Chain Rule

Problem 4YT: YOUR TURN Find dy/dx if y=5x2-6x-2.

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Question

Evaluate the given integral where C is the left half of the unit circle in ccd.

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

Expert Solution

Step 1

Note:- In given problem you mention "ccd" but one short form has different different full form. So, please always complete word so that we could use exactly that method. Thank you

Given integral is

$\int_{C} z \sin (z^{2}) d z$

C is left half of the unit circle.

For a circle, $z = r e^{i θ}$

As, given circle is unit circle so $r = 1$ then

$z = e^{i θ}; \frac{- π}{2} \leq θ \leq \frac{π}{2}$