Answer
$3$
Work Step by Step
Apply Formula (5)
$\displaystyle \iint_{R}g(x)h(x)dA=\int_{a}^{b}g(x)dx\int_{c}^{d}h(y)dy, \quad$ where $R=[a,b]\times[c,d]$.
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$\displaystyle \int_{\pi/6}^{\pi/2}\int_{-1}^{5}\cos ydxdy =\displaystyle \int_{-1}^{5}(1)dx\int_{\pi/6}^{\pi/2}\cos ydy$
$=[x]_{-1}^{5}\cdot[\sin y]_{\pi/6}^{\pi/2}$
$=[5-(-1)](\displaystyle \sin\frac{\pi}{2}-\sin\frac{\pi}{6})$
$=6(1-\displaystyle \frac{1}{2})$
$=3$
