Question

(1) Compute the line integral $\int_c -y \,dx + x \,dy$, where C is a circle of radius r about the origin, travelled in a counterclockwise direction. What happens if you travel around C clockwise? (2) Compute the line integral $\int_c \frac{-y \,dx + x \,dy}{x^2 + y^2}$ where C is a circle of radius r about the origin, travelled in a counterclockwise direction. What happens if you travel around C clockwise?

          (1) Compute the line integral $\int_c -y \,dx + x \,dy$, where C is a circle of radius r about the origin, travelled in a counterclockwise direction.
What happens if you travel around C clockwise?
(2) Compute the line integral
$\int_c \frac{-y \,dx + x \,dy}{x^2 + y^2}$
where C is a circle of radius r about the origin, travelled in a counterclockwise direction.
What happens if you travel around C clockwise?

(1) Compute the line integral -y dx + x dy, where C is a circle of radius r about the origin, travelled in a counterclockwise direction.
What happens if you travel around C clockwise?
(2) Compute the line integral
(-y dx + x dy)/(x^2 + y^2)
where C is a circle of radius r about the origin, travelled in a counterclockwise direction.
What happens if you travel around C clockwise?

Added by Silvia M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

06/28/2022

Step 1

Let's parameterize the circle C as x = r*cos(t) and y = r*sin(t), where t ranges from 0 to 2π. Show more…

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