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Question Number 128620 by Ahmed1hamouda last updated on 08/Jan/21

	Answered by TheSupreme last updated on 09/Jan/21
	$u=x+y v=x−y x=((u+v)/2) y=((u−v)/2) J= [(((1/2) (1/2))),(((1/2) −(1/2))) ] det(J)=−(1/2) R={(u,v)∣−1≤v≤1,1≤u≤3} ∫∫u^2 sin(v)(−(1/2))dudv=(u^3 /6)∣_1 ^3 cos(v)∣_(−1) ^1 =((26)/6)2cos(1)=((26)/3)cos(1)$
	$u = x + y$ $v = x - y$ $x = \frac{u + v}{2}$ $y = \frac{u - v}{2}$ $J = [\begin{matrix} \frac{1}{2} \frac{1}{2} \\ \frac{1}{2} - \frac{1}{2} \end{matrix}]$ $d e t (J) = - \frac{1}{2}$ $R = {(u, v) ∣ - 1 ⩽ v ⩽ 1, 1 ⩽ u ⩽ 3}$ $\int \int u^{2} s i n (v) (- \frac{1}{2}) d u d v = \frac{u^{3}}{6} ∣_{1}^{3} c o s (v) ∣_{- 1}^{1}$ $= \frac{26}{6} 2 c o s (1) = \frac{26}{3} c o s (1)$
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