Question

Marque a alternativa que corresponde a área da região limitada entre as funções x + y = 3 e y +x² = 3
a) 2 u.a
b) 9/2 u.a
c) 1/6 u.a
d) 4/3 u.a
e) 2/5 u.a

Answer 1

Intervalo:

$y= 3-x$

$y= 3-x^{2}$

$3-x = 3-x^{2}$

$3-x = 3-x^{2}$

$x^{2} = x$

$x = 1$

ou

$x = 0$

$\int\limits^1_0 {(3-x^{2}) - (3-x)} \, dx = \int\limits^1_0 {-x^{2}+x} \, dx$

$\int\limits^1_0 {-x^{2}+x} \, dx = - (\frac{x^{3}}{3} )+ (\frac{x^{2}}{2})$

$- (\frac{x^{3}}{3} )+ (\frac{x^{2}}{2}) = [- (\frac{1^{3}}{3} )+ (\frac{1^{2}}{2})]-[- (\frac{0^{3}}{3} )+ (\frac{0^{2}}{2})]$

$- \frac{1}{3} + \frac{1}{2} = \frac{1}{6} u.a.$

a) 2 u.a

b) 9/2 u.a

c) 1/6 u.a ←←←

d) 4/3 u.a

e) 2/5 u.a