Question

$\int\limits^2_0 { \int\limits^1_0 {y}\ sen\ x\ \, dy } \, dx \ ,\ qual\ seu\ valor\ aproximado\ ?$

a) 0,7
b) 0
c) 0,3
d) -0,2
e) 0,5

Answer 1

$\\ \int\limits^2_0 {} \, \int\limits^1_0 {} \, ySen(x)dydx = \int\limits^2_0 {} \, \frac{y^2Sen(x)}{2} |(0,1)dx \\ \\ = \int\limits^2_0 {} \, \frac{Sen(x)}{2}dx \\ \\ = \frac{1}{2} \int\limits^2_0 {} \, Sen(x)dx \\ \\ = \frac{1}{2} (-Cos(x))|(0,2) \\ \\ = \frac{1}{2} (-Cos(2) - (-Cos(0) ) \\ \\ = \frac{1}{2} (1-Cos(2))$

≈ 0