Question

Evaluate the integral by making an appropriate change of variables.\\ $\iint_R 5 \sin(49x^2 + 4y^2) dA$, where $R$ is the region in the first quadrant bounded by the ellipse $49x^2 + 4y^2 = 1$

          Evaluate the integral by making an appropriate change of variables.\\
$\iint_R 5 \sin(49x^2 + 4y^2) dA$, where $R$ is the region in the first quadrant bounded by the ellipse $49x^2 + 4y^2 = 1$

Evaluate the integral by making an appropriate change of variables.

5 sin(49x^2 + 4y^2) dA, where R is the region in the first quadrant bounded by the ellipse 49x^2 + 4y^2 = 1

Added by Brent V.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

04/06/2023

Step 1

Let's make the following change of variables: u = 7x v = 2y This change of variables will transform the ellipse equation into a unit circle equation: 49(7x)^2 + 4(2y)^2 = 1 49u^2 + 4v^2 = 1 Also, the differential area element dA will transform as follows: dA = Show more…

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e integral by making an appropriate change of variables. ∬_(R)5sin(49x^(2)+4y^(2))dA, where R is the region in the first quadrant bounded by the ellipse 49x^(2)+4y^(2)=1 e integral by making an appropriate change of variables