Question

Use the transformation u=2x+3y, v=x+4y to evaluate the given integral for the region R bounded by the lines y=(-2/3)x+1, y=(-2/3)x+4, y=(-1/4)x, and y=(-1/4)x+2. int int[R](2x^2 +11xy +12y^2) dx dy

Answer 1

\[Transformations: \ u=2x+3y, \ v=x+4y\]\[Bounded \ by: \\ y= \dfrac{-2}{3}x+1, \\ y= \dfrac{-2}{3}x+4, \\ y= \dfrac{-1}{4}x, \\ y= \dfrac{-1}{4}x+2\] \[Given \ Integral: \ \int\limits_{}^{}\int\limits_{R}^{}2x ^{2}+11xy+12y ^{2} \ dx dy\]