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Improper Integral

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Question 1

The value of the following improper integral is [Tex]\,\int\limits_0^1 {x\,\log \,x\,dx} = \_\_\_\_\_.[/Tex]

  • [Tex]{1 \over 4}[/Tex]

  • [Tex]0[/Tex]

  • [Tex]{{ - 1} \over 4}[/Tex]

  • [Tex]1[/Tex]

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Question 2

The integral [Tex] \int_{1}^{\infty} \frac{1}{x^p}\,dx[/Tex] converges if and only if

  • A. p<1p < 1p<1

  • B. p=1p = 1p=1

  • p > 1

  • p = 0

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Question 3

The integral [Tex]\int_{1}^{\infty} \frac{1}{x} \,[/Tex] is

  • Convergent

  • Divergent

  • Undefined

  • Equal to 1

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Question 4

Evaluate: [Tex]\int_{1}^{\infty} \frac{x+1}{x^3} \, dx[/Tex]

  • 3/2

  • 1

  • 2

  • Divergent

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Question 5

[Tex]\int_{0}^{a} \frac{1}{x^p}[/Tex] is an example of:

  • Improper integral of the first kind

  • Improper integral of the second kind

  • Proper integral

  • None of these

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Question 6

An integral with both limits finite but discontinuous integrand at some point is called:

  • Improper integral of the first kind

  • Improper integral of the second kind

  • Proper integral

  • Definite integral

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There are 6 questions to complete.

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