*Q4: [Exercise 30] By making the coordinate transformation y u(x, y) = x + ², v(x, y) = 22²₁ 2 evaluate the double integral x + y 1-] (7³) sin v). I = where A is the triangular region Y COS (¹7) de dy. (* dx Т with vertices at (x, y) = (0,0), (2,0) and (1,1). Extra: can you verify your answer by evaluating I directly without this transforma- tion?

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Chapter2: Second-order Linear Odes
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*Q4: [Exercise 30] By making the coordinate transformation
x + y
2
u(x, y)
evaluate the double integral
where A is the triangular region
tion?
=
v(x, y)
Y
=
-
x y
1 = [[ sin (= +") cos (²7") dr dy.
I
2
2
x - Y
2
→ X
2
with vertices at (x, y) = (0,0), (2,0) and (1,1).
Extra: can you verify your answer by evaluating I directly without this transforma-
Transcribed Image Text:*Q4: [Exercise 30] By making the coordinate transformation x + y 2 u(x, y) evaluate the double integral where A is the triangular region tion? = v(x, y) Y = - x y 1 = [[ sin (= +") cos (²7") dr dy. I 2 2 x - Y 2 → X 2 with vertices at (x, y) = (0,0), (2,0) and (1,1). Extra: can you verify your answer by evaluating I directly without this transforma-
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