Integration

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Question 1

Given i=√-1, what will be the evaluation of the integral [Tex]\int_{0}^{\pi/2} \frac{\cos x + i\sin x}{\cos x - i\sin x} dx[/Tex]?
 

  • -i
     

  • 2
     

  • 0
     

  • i
     

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Question 2

[Tex]\int_{0}^{\pi/4} \frac{1 - \tan x}{1 + \tan x} dx[/Tex] is equivalent to

  • 0

  • 1

  • ln 2

  • 1/2 ln 2

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Question 3

If [Tex]\int_{0}^{2\pi} |x \sin x| dx = k \pi,[/Tex] then the value of k is equal to _____.

  • 2

  • 3

  • 4

  • 5

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Question 4

The value of the integral given below is:

[Tex]\int_{0}^{\pi} x^2 \cos x dx[/Tex]

  • -2π

  • π

  • -π

  • 2π

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Question 5

If for non-zero x,

a f(x) + bf(1/x) = 1/x - 25 where (a ≠ b ), then [Tex]\int_{1}^{2} f(x) ~dx[/Tex] is:

  • [Tex]\frac{1}{a^2 - b^2} \left[ a(\ln 2 - 25) + \frac{47b}{2} \right][/Tex]

  • [Tex]\frac{1}{a^2 - b^2} \left[ a(2 \ln 2 - 25) - \frac{47b}{2} \right][/Tex]

  • [Tex]\frac{1}{a^2 - b^2} \left[ a(2 \ln 2 - 25) + \frac{47b}{2} \right][/Tex]

  • [Tex]\frac{1}{a^2 - b^2} \left[ a(\ln 2 - 25) - \frac{47b}{2} \right][/Tex]

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Question 6

Find the Integral value of f(x) = x × sin x within the limits 0, and π.

  • π

  • 2π

  • π/2

  • 0

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Question 7

The value of the definite integral 

 

 is _______. (Rounded off to the nearest integer)

  • 0
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Question 8

What is the value of

 
  • 2
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Question 9

Evaluate the integral

 

  • (π ln 2)/4

  • (ln 2)/2

  • (ln22)/2

  • (π ln 2)/8

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Question 10

 

  • 0

  • 1

  • ln 2

  • (ln 2)/2

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Tags:
GATE CS

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