Question

Evaluate the iterated integral by converting to polar coordinates. int_0^9 int_0^(sqrt(81-x^(2))) e^(-x^(2)-y^(2))dydx Evaluate the iterated integral by converting to polar coordinates /81 = 2

Name: evaluate the iterated integral by converting to polar coordinates int09 int0sqrt81 x2 e x2 y2dydx evaluate the iterated integral by converting to polar coordinates 81 2 94346
Uploaded: 2022-05-29T17:27:06-08:00
Duration: 3 min 4 s
Channel: Shaiju T
Description: evaluate the iterated integral by converting to polar coordinates int09 int0sqrt81 x2 e x2 y2dydx evaluate the iterated integral by converting to polar coordinates 81 2 94346

          Evaluate the iterated integral by converting to polar coordinates.
int_0^9 int_0^(sqrt(81-x^(2))) e^(-x^(2)-y^(2))dydx
Evaluate the iterated integral by converting to polar coordinates
 /81 = 2

evaluate the iterated integral by converting to polar coordinates int09 int0sqrt81 x2 e x2 y2dydx evaluate the iterated integral by converting to polar coordinates 81 2 94346

Added by Dalton F.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Shaiju T

05/29/2022

Step 1

Let's first rewrite the given integral in terms of polar coordinates. In polar coordinates, we have: x = r*cos(theta) y = r*sin(theta) Also, the Jacobian for converting from Cartesian to polar coordinates is r. Therefore, the integral becomes: ∫∫ e^(-r^2) * r dr Show more…

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Evaluate the iterated integral by converting to polar coordinates. int_0^9 int_0^(sqrt(81-x^(2))) e^(-x^(2)-y^(2))dydx Evaluate the iterated integral by converting to polar coordinates /81 = 2