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MHT CET202311 May 2023Evening ShiftMathematicsIndefinite IntegrationActual

If I = ( (x)) d x , then I is given by

Options

  1. A- x 2 ( ( x)- ( x))+ c , where c is a constant of integration.
  2. Bx 2 ( ( x)- ( x))+ c , where c is a constant of integration.
  3. Cx 2 ( ( x)+ ( x))+ c , where c is a constant of 'integration.
  4. D- x 2 ( ( x)+ ( x))+ c , where c is a constant of integration.

Correct answer

B. x 2 ( ( x)- ( x))+ c , where c is a constant of integration.

Step-by-step solution

Let x= t x= e ^ t Differentiating w.r.t. t, we get d x= e ^ t dt aligned I & = ( t ) e ^ t dt & = t e ^ t - t e ^ t dt & = t e ^ t - [ t e ^ t + t e ^ t dt ] & = t e ^ t - t e ^ t - I aligned array ll & 2 I =x ( x)-x ( x)+ c & I = x 2 ( ( x)- ( x))+ c array

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