The integrating factor of the differential equation3xlogexdydx&nb

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

71.

The value of the integral π6π21 +sin2x + cos2xsinx + cosxdx is equal to

  • 16

  • 8

  • 4

  • 1


72.

The value of the integral 0π211 +tanx101dx is equal to

  • 1

  • π6

  • π8

  • π4


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73.

The integrating factor of the differential equation

3xlogexdydx + y = 2logex is given by

  • logex3

  • logelogex

  • logex

  • logex13


D.

logex13

Given, 3xlogexdydx + y = 2logex

Dividing both sides by 3xloge(x), we get

      dydx + 13xlogexy = 2logex3xlogex dydx + 13xlogexy = 23x

which is linear form dydx + Py = Q, where P and Q are function of x and the integrating factor is given by the following formula ePdx

         IF = e13xlogexdxPut logex = t     1xdx = dt       IF = e13dtt = e13logt                = elogt13                = t13                 = logex13


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74.

The value of the integral 0π4sinx + cosx3 + sin2xdx is equal to

  • loge2

  • loge3

  • 14loge2

  • 14loge3


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75.

The value of the integral - 221 + 2sinxexdx is equal to

  • 0

  • e2 - 1

  • 2(e2 - 1)

  • 1


76.

The area of the region bounded by the curves y = x , y = 1x, x = 2 is

  • 4 - loge2

  • 14 + loge2

  • 3 - loge2

  • 154 - loge2


77.

Let y be the solution of the differential equation

xdydx = y21 - ylogx satisfying y(1) = 1. Then, y satisfies

  • y = xy - 1

  • y = xy

  • y = xy + 1

  • y = xy + 2


78.

The area of the region, bounded by the curves y = sin- 1(x) + x(1 - x) and y = sin- 1 (x) - x(1 - x) in the first quadrant, is

  • 1

  • 12

  • 13

  • 14


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79.

The value of the integral 15x - 3 + 1 - xdx is equal to

  • 4

  • 8

  • 12

  • 16


80.

Let [x] denote the greatest integer less than or equal to x, then the value of the integral - 11x - 2xdx is equal to

  • 3

  • 2

  • - 2

  • - 3


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