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Multivariable Calculus

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Difficult

Double Integral with Absolute Function

MVCALC-DJGKBA

Evaluate the double integral:

$$\iint_R \sqrt{|y-x^2|}dA$$

...where:

$$R=\{(x,y): -1\leq x\leq 1, 0\leq y\leq 1\}$$

A

$\cfrac{\pi}{2}+1$

B

$\cfrac{1}{3}+\cfrac{\pi}{4}$

C

$\cfrac{\pi}{3}+\cfrac{1}{4}$

D

$\sin 1 + \ln \pi$

E

$1+\pi$