The value of the integral ∫- π4π4sin- 4x

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

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81.

The value of the integral - π4π4sin- 4xdx is

  • - 83

  • 32

  • 83

  • None of these


A.

- 83

LetI = - π4π4sin-4xdx= - π4π41sin4xdx= - π4π4csc4xdx = - π4π4csc2x2dx= - π4π41 + cot2xcsc2xdxPut cotx = t - csc2xdx = dt I = - 111 + t2dt= - 2011 + t2dt= - 2t + t3301= - 21 + 13= - 83


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82.

The solution of the differential equation xdy - ydx = x2 + y2dx is

  • x + x2 + y2 = cx2

  • y - x2 + y2 = cx2

  • x - x2 + y2 = cx

  • y + x2 + y2 = cx2


83.

The differential equation of all non-vertical lines in a plane is

  • d2ydx2 = 0

  • d2xdy2 = 0

  • dydx = 0

  • dxdy = 0


84.

x + 2x + 42exdx is equal to

  • exxx + 4 +C

  • exx + 2x + 4 +C

  • exx - 2x + 4 +C

  • ex2xexx + 4 +C


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85.

The value of 35x2x2 - 4dx

  • 2 - loge157

  • 2 + loge157

  • 2 + 4loge3 - 4loge7 + 4loge5

  • 2 - tan-157


86.

0dxx +x2 +13 is equal to

  • 38

  • 18

  • - 38

  • None of these


87.

A common tangent to 9x2 - 16y2 = 144 and x2 + y2 = 9 is

  • y = 37x + 157

  • y = 327x + 157

  • y = 237x + 157

  • None of these


88.

The differential equation of all parabolas whose axes are parallel to y-axis is

  • d3ydx3 = 0

  • d2xdy2 = 0

  • d3ydx3+ d2xdy2 = 0

  • d2ydx2 + 2dydx = 0


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89.

The locus of a point P which moves such that 2PA = 3PB, where A(0, 0) and B(4,- 3) are points, is

  • 5x2 - 5y2 - 72x + 54y + 225 = 0

  • 5x2 + 5y2 - 72x + 54y + 225 = 0

  • 5x2 + 5y2 + 72x - 54y + 225 = 0

  • 5x2 + 5y2 - 72x - 54y - 225 = 0


90.

The points P is equidistant from A(1, 3), B (- 3, 5) and C(5, - 1), then PA is equal to

  • 5

  • 55

  • 25

  • 510


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