Question

Use the transformation $T:u=\frac{1}{2}x$ and $v=\frac{1}{3}y$ to evaluate the integral $R \int \int x^2 dA$ where is the region bounded on the   by the ellipse  $9x^2+4y^2=36.$ Let S be the image of R under T on the  . Sketch regions R and S. Set up the integral as an iterated integral of a function over region S. Use technology to evaluate the integral. Give the exact answer.

Answer 1

SS oxdA. R the elliplee where R is the region bounded by 9x² + 4y² = 36. (0,3) + 9 R. 12,0) het 7: UP will 0,-3) x = 24, y = 34. -22 x 22 -1 2 4 L -32 y = 3 =-kusi 2 Tacobian cau, ) S R (10) » SS x² dA = SS 442 put | dudee, where si u't u²=1 6 SS qu² dude -4 = 655"' 47"roko odreds = 63 20 27 / 0 (0.8²0 do 082" (0²0 do It Cosao sinad T do ot Z 3 x 2T is x² dA = 6T T