Saved Bookmarks
| 1. |
Determine:(a) \( \int_{0}^{\sqrt{3}+2} \int_{0}^{\pi / 3}(2 \cos \theta-3 \sin 3 \theta) d \theta d r \) |
|
Answer» \(\int \limits _0 ^{\sqrt3 +2} \left[ \int \limits_0^{\frac \pi 3}(2\, cos \, \theta - 3 \, sin \, 3 \, \theta)d\theta\right]dr\) = \(\int \limits_0^{\sqrt3 +2}dr \left[ 2\, sin \, \theta + cos \, 3 \theta \right]_0^{\frac \pi 3}\) = \(\left[r\right]_0^{\sqrt3 +2} \) ( 2 sin \(\frac \pi 3\) + cos \(\pi\) - 2 sin 0 - cos 0) = (\(\sqrt3 \) + 2 -0) ( 2 x \(\frac {\sqrt3}{2}\) -1 -1) = (\(\sqrt 3\) +2) ( \(\sqrt 3\) -2) = 3-4 = -1 |
|