Question

V. Evaluate $\int_C |z|^2 dz$, where C is $x(t) = t^2$, $y(t) = \frac{1}{t}$, $t: 1 \to 3$ VI. Evaluate $\int_C (\bar{z})^2 dz$ on the contour shown here $\implies$ VII. Find $I = \int_C |iz^2| dz$ where C is the upper half of the ellipse $\frac{(Re \ z)^2}{4} + \frac{(Im \ z)^2}{9} = 1$ from +2 to -2. This one is challenging. Hint #1: Use polar form of the ellipse. Hint #2: Keep the table of integrals handy.

          V. Evaluate $\int_C |z|^2 dz$, where C is $x(t) = t^2$, $y(t) = \frac{1}{t}$, $t: 1 \to 3$
VI. Evaluate $\int_C (\bar{z})^2 dz$ on the contour shown here $\implies$
VII. Find $I = \int_C |iz^2| dz$
where C is the upper half of the ellipse $\frac{(Re \ z)^2}{4} + \frac{(Im \ z)^2}{9} = 1$ from +2 to -2.
This one is challenging.
Hint #1: Use polar form of the ellipse.
Hint #2: Keep the table of integrals handy.

V. Evaluate |z|^2 dz, where C is x(t) = t^2, y(t) = (1)/(t), t: 1 → 3
VI. Evaluate (z̅)^2 dz on the contour shown here
VII. Find I = |iz^2| dz
where C is the upper half of the ellipse ((Re z)^2)/(4) + ((Im z)^2)/(9) = 1 from +2 to -2.
This one is challenging.
Hint #1: Use polar form of the ellipse.
Hint #2: Keep the table of integrals handy.

Added by Amy U.

University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Animesh Raj

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Evaluate ∫_C |z|^2 dz, where C is x(t)=t^2, y(t)=1/t, t:1->3 ** Show more…

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V. Evaluate ∫_C |z|^2 dz, where C is x(t)=t^2, y(t)=1/t, t:1->3 VI. Evaluate ∫_C (bar(z))^2 dz on the contour shown here ->-> VII. Find I=∫_C i|iz^2|dz where C is the upper half of the ellipse (Rez)^2/4+(Imz)^2/9=1 from +2 to -2. This one is challenging. Hint #1: Use polar form of the ellipse. Hint #2: Keep the table of integrals handy.