Mathematics 241 – Multivariable Calculus Makeup Quiz 8 – November 19, 2007 (the final quiz of the semester!)

Your Name:

(5) A) Evaluate ∫ ∫_{R} y + 1 dA where R is the rectangle R = [1, 2] × [0, 3] in R^{2}.

(5) B) Sketch the region of integration for the integral ∫_{0}^{1} ∫_{x}^{1+x^{2}} f(x, y) dy dx, and interchange the order of integration (i.e. rewrite the given integral as one or more integrals ∫ ∫ f(x, y) dx dy).