LISTA 2 - INTEGRAL DUPLA EM REGIÕES MAIS GERAIS

Question 1

Quais das expressões a seguir não fazem sentido?

Accepted Answer

$\int_{0}^{1}\int_{1}^{y}f(x, y)dydx$

Accepted Answer

$\int_{1}^{y}\int_{0}^{1}f(x, y)dydx$

Answer

$\int_{0}^{1}\int_{1}^{x}f(x, y)dydx$

Answer

$\int_{0}^{1}\int_{x}^{1}f(x, y)dydx$

Question 2

Qual das quatro regiões, na figura dada, é o domínio de integração de $\int_{-\sqrt{2}/2}^{0}\int_{-x}^{\sqrt{1-x^2}}f(x, y)dydx$?

Accepted Answer

B

Answer

A

Answer

C

Answer

D

Question 3

Calcule a área limitada pelas curvas $y=x^2$ e $y = x+2$.

Accepted Answer

$\frac{9}{2}$

Answer

$\frac{19}{12}$

Answer

$\frac{19}{4}$

Answer

$\frac{11}{12}$

Question 4

Calcule a área da Elipse $\frac{x^2}{16} + \frac{y^2}{25} = 1$ usando integral dupla.

Accepted Answer

$20\pi$

Answer

$10\pi$

Answer

$\pi$

Answer

20

Question 5

Determine o volume do sólido limitado pelo plano $z=0$ e pelo paraboloide $z = 4 - x^2 - y^2$

Accepted Answer

$8\pi$

Answer

$\frac{\pi}{2}$

Answer

$4\pi$

Answer

$16\pi$

Question 6

Determine o volume do sólido que está sob o paraboloide $z = x^2 + y^2$, acima do plano xy e dentro do cilindro $x^2 + y^2 = 2y$.

Accepted Answer

$\frac{3\pi}{2}$

Answer

$\frac{\pi}{2}$

Answer

$\frac{3\pi}{4}$

Answer

$\frac{\pi}{4}$

Question 7

Marque a alternativa que apresenta a integral $\int_{4}^{9}\int_{\sqrt{y}}^{y}f(x, y)dxdy$.

Accepted Answer

$\int_{2}^{3}\int_{4}^{x^2}f(x, y)dydx +\int_{3}^{4}\int_{4}^{9}f(x, y)dydx+ \int_{4}^{9}\int_{x}^{9}f(x, y)dydx$

Answer

$\int_{2}^{3}\int_{x^2}^{9}f(x, y)dxdy+\int_{3}^{9}\int_{x}^{9}f(x, y)dydx$

Answer

$\int_{2}^{3}\int_{9}^{x^2}$f(x, y)dydx

Answer

$\int_{2}^{3}\int_{9}^{x^2}$f(x, y)dxdy

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