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Multivariable Calculus

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Difficult

Change of Variable According to Integrand and Boundary

MVCALC-UQZEYZ

Evaluate the following double integral using a change of variables:

$$I=\iint_R (x-2y)\sqrt{x-3y}dA$$

...where $R$ is the triangular region $R$ bounded by $x-2y=1$, $x-3y=0$ and $y=0$.

A

$\cfrac{4}{21}$

B

$\cfrac{1}{7}$

C

$\cfrac{2}{3}$

D

$21$

E

$4\pi$