Chapter 15 - Multiple Integrals - 15.1 Double Integrals over Rectangles - 15.1 Exercises - Page 1040: 18

$$0.7336$$

$$Question: \int_0^{\pi /6} \int_0^{\pi /2}(sinx +siny)dydx$$ $Solution:$ $=\int_0^{\pi /6}(ysinx-cosy)_0^{\pi /2}dx$ $=\int_0^{\pi /6}[(\frac{\pi}{2}sinx-0)-(0-1)]dx$ $=\int_0^{\pi /6}(\frac{\pi}{2}sinx+1)dx$ $=(-\frac{\pi}{2}cosx+x)_0^{\pi /6}dx$ $= (-0.8364)-(-1.57)$ $$Answer\approx0.7336$$