jonatas Vieira
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Nessa Lista vamos trabalhar a resolução de integrais duplas sobre regiões retangulares. Além de fixar o conceito de integral iterada, buscamos revisar técnicas de integração.

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BOTE FÉ NA MATEMÁTICA
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jonatas Vieira
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Lista 1: Integral Dupla Sobre Retângulo

Lista 1: Integral Dupla Sobre Retângulo

Question 1 of 6

1

Calcule a integral iterada \(\int_{1}^{3}\int_{0}^{1}(1+4xy)dxdy\)

Select one of the following:

  • 10

  • 0

  • 12

  • 3

Explanation

Question 2 of 6

1

Calcule a integral iterada \(\int_{0}^{\pi/2}\int_{0}^{\pi/2} sen(x).cos(y)dydx\)

Select one of the following:

  • 1

  • 10

  • 0

  • 5

Explanation

Question 3 of 6

1

Calcule a integral iterada \(\int_{0}^{2}\int_{0}^{1}(2x+y)^8dxdy\).

Select one of the following:

  • \(\frac{2^{20} - 2^{11}}{180}\)

  • \(\frac{2^{10}}{180}\)

  • \(\frac{1}{9}\)

  • 1024

Explanation

Question 4 of 6

1

Calcule a integral iterada \(\int_{0}^{1}\int_{1}^{2}\frac{xe^x}{y}dydx\)

Select one of the following:

  • \(\ln(2)\)

  • 0

  • 1

  • \(e\ln(2)\)

Explanation

Question 5 of 6

1

Calcule a integral dupla \(\int\int_{R}\frac{xy^2}{x^2+1}dA\), onde \(R = \{(x, y)\in \mathbb{R}^2; 0\leq x \leq 1, \, -3\leq y\leq 3\}\)

Select one of the following:

  • \(9\ln(2)\)

  • \(\ln(2)\)

  • \(18\ln(2)\)

  • 9

Explanation

Question 6 of 6

1

Calcule a integral dupla \(\int\int_{R}xye^{x^2y}dA\), onde \(R = [0,1]\times[0,2]\).

Select one of the following:

  • \(\frac{e^2 - 3}{2}\)

  • \(\frac{e}{2} \)

  • \(\frac{e}{2} - 2\)

  • \(e - 1\)

Explanation

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