Question

Problem 3: Calculate the integral $$ \iint_D \frac{x}{x^2 + y^2} dA $$ where $D$ is the part of the ring $1 \le x^2 + y^2 \le 9$ in the second quadrant.

Name: problem 3 calculate the integral iintd fracxx2 y2 da where d is the part of the ring 1 le x2 y2 le 9 in the second quadrant 67655
Uploaded: 2023-12-02T23:41:39-08:00
Duration: 5 min 51 s
Channel: Vincenzo Zaccaro
Description: problem 3 calculate the integral iintd fracxx2 y2 da where d is the part of the ring 1 le x2 y2 le 9 in the second quadrant 67655

          Problem 3: Calculate the integral
$$ \iint_D \frac{x}{x^2 + y^2} dA $$
where $D$ is the part of the ring $1 \le x^2 + y^2 \le 9$ in the second quadrant.

$problem 3 calculate the integral iintd fracxx2 y2 da where d is the part of the ring 1 le x2 y2 le 9 in the second quadrant 67655$

Added by Michelle W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vincenzo Zaccaro

12/02/2023

Step 1

We use polar coordinates: $x = r \cos \theta$, $y = r \sin \theta$, $dA = r dr d\theta$. Then $1 \le r^2 \le 9$, so $1 \le r \le 3$. Since $D$ is in the second quadrant, $\frac{\pi}{2} \le \theta \le \pi$. Therefore, $$ I = \int_{\pi/2}^\pi \int_1^3 \frac{r \cos Show more…

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Problem 3: Calculate the integral $$ \iint_D \frac{x}{x^2 + y^2} dA $$ where $D$ is the part of the ring $1 \le x^2 + y^2 \le 9$ in the second quadrant.