Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §14.2 Change to Better Coordinates, #34 · Multivariable Calculus · Change of variables

True or false, with a reason: (a) If the … region …

True or false, with a reason:
(a) If the $uv$ region $S$ corresponds to the $x y$ region $R$ , then area of $S$ = area of $R$ .
(b) $\iint x d A \leq \iint x^{2} d A$
(c) The average value of $f (x, y)$ is $\iint f (x, y) d A$
(d) $\int_{- \infty}^{\infty} x e^{- x^{2}} d x = 0$
(e) A polar rectangle has the same area as a straight-sided region with the same corners.

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §14.2 Change to Better Coordinates, #34

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