Thevalue of integral ∫0π2tanx + cotxdx 

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 Multiple Choice QuestionsMultiple Choice Questions

581.

dxxxn + 1 is equal to

  • 1nlogexnxn + 1 + C

  • - 1nlogexn + 1xn + C

  • 1nlogexnxn + 1 + C

  • None of the above


582.

Evaluate dxxx5 + 2

  • 110logx5 + 1x5 + 2 + C

  • 15logx5x5 + 2 + C

  • 110logx5x5 + 2 + C

  • 110logx5 + 1x5 + 2 + C


583.

23x5 - x + xdx is equal to

  • 14

  • 1

  • 32

  • 12


584.

I = - 11x2 + sinx1 + x2dx

  • 0

  • 2 + π2

  • 2 - π2

  • π2 - 2


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585.

A curve is drawn to pass through the points given by the following table.
x 1 1.5 2 2.5 3 3.5 4
y 2 2.4 2.7 2.8 3 2.6 2.1

Using Simpson's 1/3rd rule, estimate the area bounded by the curve, the x-axis and the lines x = 1, x = 4

  • 7.47 sq units

  • 7.76 sq units

  • 7.78 sq units

  • 7.82 sq units


586.

Which of these methods for numerical integration is also called as parabolic formula?

  • Simpson's one-third rule

  • Simpson's three-eighth's rule

  • Trapezoidal rule

  • None of the above


587.

Calculate by Trapezoidal rule an approximate value of - 33x4dx by taking seven equidistant ordinates

  • 98

  • 97.2

  • 100

  • 115


588.

The value of 01sin-1xdx is

  • π2

  • π2 - 1

  • π2 + 1

  • 0


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589.

By Simposon's rule taking n = 4, the value of the integral 01dx1 + x2 is equal to

  • 0.785

  • 0.788

  • 0.781

  • None of these


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590.

Thevalue of integral 0π2tanx + cotxdx is

  • 2π

  • π

  • π2

  • 0


A.

2π

Ley I = 0π2tanx + cotxdx If 02afx = 02af2a - x,then 02afxdx = 20afxdx I = 20π4tanx + cotxdx       = 20π4sinxcosx + cosxsinxdx       = 20π4sinx + cosxsinxcosxdx       = 220π4sinx + cosx2sinxcosxdx

(on multiplying numerator and denominator by 2)       = 220π4sinx + cosx1 - sinx - cosx2dx sinx - cosx2 = sin2x + cos2x - 2sinxcosx 2sinxcosx = 1 - sinx - cosx2Put sinx - cosx = t  cosx + sinx = dtdx dx = dtcosx + sinx I = 22- 10dt1 - t2       = 22sin-1t- 10       = 22sin-10 - sin-1- 1       = 220 + sin-11       = 22π2       = 2π


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