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yazzyv05
10.04.2020 •
Mathematics
Evaluate the given integral by making an appropriate change of variables, where R is the region in the first quadrant bounded by the ellipse 64x2 + 81y2 = 1. $ L=\iint_{R} {\color{red}9} \sin ({\color{red}384} x^{2} + {\color{red}486} y^{2})\,dA $.
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Ответ:
Notice that Given that
is an ellipse, consider a conversion to polar coordinates:
The Jacobian for this transformation is
with determinant![\det J=\frac r{72}](/tpl/images/0594/1021/f036c.png)
Then the integral in polar coordinates is
where you can evaluate the remaining integral by substituting
and
.
Ответ: