2. Consider the region R in the xy-plane given by R = {(x, y) = R² x ≥ 0, y ≥ 0 and 1 ≤ x² + y² ≤2} . (a) Sketch the region R. (b) By changing to polar coordinates evaluate the double integral y sin (7 (x² + y²)) dr dy. x² + y² Recall that Cartesian and polar coordinates are related by (x, y) =(r cos 0, r sin 0), (1) where r = √√√x²+ y², and 0 ≤ 0 < 2π. You may assume that the Jacobian for the change of variables (1) is given by (x, y) 富 =r. ǝ (r, 0)

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Please solve this question it has sub parts to it. Appreciate your time. Also consider what the question is specifically asking. And please integrate in parts. And whatever method the question is suited for. After finalising the working out please double check. Just to be sure!. The quality of the working out. I'll give it a downvote or a upvote. Appreciate your time!. 

2. Consider the region R in the xy-plane given by
R = {(x, y) = R² x ≥ 0, y ≥ 0 and 1 ≤ x² + y² ≤2} .
(a) Sketch the region R.
(b) By changing to polar coordinates evaluate the double integral
y sin (7 (x² + y²)) dr dy.
x² + y²
Recall that Cartesian and polar coordinates are related by
(x, y) =(r cos 0, r sin 0),
(1)
where r = √√√x²+ y², and 0 ≤ 0 < 2π. You may assume that the
Jacobian for the change of variables (1) is given by
(x, y)
富
=r.
ǝ (r, 0)
Transcribed Image Text:2. Consider the region R in the xy-plane given by R = {(x, y) = R² x ≥ 0, y ≥ 0 and 1 ≤ x² + y² ≤2} . (a) Sketch the region R. (b) By changing to polar coordinates evaluate the double integral y sin (7 (x² + y²)) dr dy. x² + y² Recall that Cartesian and polar coordinates are related by (x, y) =(r cos 0, r sin 0), (1) where r = √√√x²+ y², and 0 ≤ 0 < 2π. You may assume that the Jacobian for the change of variables (1) is given by (x, y) 富 =r. ǝ (r, 0)
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