Question

1. Evaluate the given integral by making an appropriate change of variables, where R is the region in the first quadrant bounded by the ellipse 36x^2+25y^2=1. L= double integral R (4sin(144x^2+100y^2) dA.

2. Use the given transformation to evaluate the given integral, where R is the region in the first quadrant bounded by the lines y = x and y = 6x and the hyperbolas xy = 1 and xy = 6. L= double integral R (8xy)dA x=u/v, y=v

3. Evaluate the given integral by making an appropriate change of variables, where R is the trapezoidal region with vertices (9, 0), (10, 0), (0, 10), and (0, 9). L= double integral R (5cos(5y-x/y+x)) dA