Question-128620

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 = \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)