Double Integrals? Double the Fun!

Calculus Level 3

Let $R$ be the region bounded by $2 \leq x \leq 4$ and $\frac{x}{2} \leq y \leq \sqrt{x}$ . What is the value of

$N = \iint_R xy\ dA ?$

The answer is 1.833333.

1 solution

Lucas Tell Marchi
Jan 28, 2014

$\int_{2}^{4}\int_{\frac{x}{2}}^{\sqrt{x}} (xy) dy dx = \int_{2}^{4} x \left ( \frac{y^{2}}{2} \right )_{\frac{x}{2}}^{\sqrt{x}} dx = \int_{2}^{4} \left ( \frac{x^{2}}{2} - \frac{x^{3}}{8} \right ) dx = \frac{33}{18} \cong 1.83$

Double Integrals? Double the Fun!

The answer is 1.833333.

1 solution

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