Math 32B midterm 1 flashcards

Math 32B flashcards for midterm 1 these are mostly for personal use

the double integral over region D of C x dA

C x area(D)

If f(x, y) is continuous over D, then it is

integrable

Fubini’s theorem

you can switch the order of integration

odd function

x^n where n is odd; f(x) = -f(-x); sin(x)

even function

x^n where n is even; f(x) = f(-x); cos(x)

average value

integral of function divided by integral of 1

polar coordinates

x = rcos(theta), y = rsin(theta), r² = x² + y², tan(theta) = y / x

polar coordinate change of variables

convert everything and multiply integrand by r

cylindrical coordinates

(r, theta, z)