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Multivariable Calculus

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Moderate

Compare Double Integrals

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Compare the following two integrals and decide which on is bigger:

$$I_1 = \iint_R (x^2-y^2)dA, \qquad I_2=\iint_R \sqrt{x^2-y^2}dA$$

...in which $R$ is the triangle zone with vertices $(0,0)$, $(1,-1)$ and $(1,1)$.

A

$I_1 \geq I_2$

B

$I_1 \leq I_2$

C

$I_1 = I_2$

D

Sometimes $I_1\geq I_2$, sometimes $I_1\leq I_2$

E

None of the above