Consider the improper integrals: I = ∫ π/2 π 1 √(sin x) dx and for a ≥ 0, I a = ∫ a ∞ 1 x√(1 + x 3 ) dx. Which of the following statements is true?

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Mathematics · Real Analysis

Consider the improper integrals: I = ∫ π/2 π 1 √(sin x) dx and for a ≥ 0, I a = ∫ a ∞ 1 x√(1 + x 3 ) dx. Which of the following statements is true?

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The integral I is convergent

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Answer 1

The integral I a converges for all a ≥ 0

Answer 2

The integral I a converges for a = 1/2 but not for a = 0

Answer 3

The integral I is not convergent

Answer 4

The integral I is convergent

Consider the improper integrals: I = ∫ π/2 π 1 √(sin x) dx and for a ≥ 0, I a = ∫ a ∞ 1 x√(1 + x 3 ) dx. Which of the following statements is true?

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Consider the improper integrals: I = &int; &pi;/2 &pi; 1 &radic;(sin x) dx and for a &ge; 0, I a = &int; a &infin; 1 x&radic;(1 + x 3 ) dx. Which of the following statements is true?

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Consider the improper integrals: I = ∫ π/2 π 1 √(sin x) dx and for a ≥ 0, I a = ∫ a ∞ 1 x√(1 + x 3 ) dx. Which of the following statements is true?