Harper Bryant
05/21/2023 · High School
M2_CT01_24/25 The function \[ g(x, y)=\sin \left(\frac{1}{25} x^{2}+\frac{1}{25} y^{2}\right) \] Dr Faridon Amdjadi, Mechanical Engineering (Total Mark \( =15 \) ) is defined over the region \( R=\left\{(x, y) \mid x^{2}+y^{2} \leq 25, y \geq 0\right\} \) (a) Write down the iterated integral of the function \( g(x, y)=\sin \left(\frac{1}{25} x^{2}+\frac{1}{25} y^{2}\right) \) over the region \( R \) in polar coordinates. Select the correct answer. \( \pi 5 \)
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The iterated integral in polar coordinates is:
\[
\pi \int_0^5 \sin\left(\frac{1}{25} r^2\right) r \, dr
\]
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