MAT-2130 Midterm: MATH 2130 App State Spring2012 Test3
Document Summary
Be sure to show your work: (14 points) consider z 4. Sketch the region of integration and then evaluate the integral. Hint: r sin(y3) dy is impossible to evaluate. sin(y3) dy dx. Reading the bounds of integration we get: x y 2 and 0 x 4 (notice the region is above the square root). We need to reverse the order of integration so that we can evaluate the integral. As a type ii region, we have 0 x y2 and 0 y 2 (remember left-to-right and then bottom-to-top). State a change of coordinates: u =??? and v =??? so that the resulting integral can be evaluated. Perform the change of coordinates, but do not evaluate the integral. The obvious change of variables (which simpli es the integral) is u = 2x + y and v = 3x y. det (inverse jacobian matrix) = det(cid:18)(cid:20)ux uy.
