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BITSAT2010MathematicsArea Under CurvesActual

If ( I _ m = ₁^ e ( x )^ m dx ), where ( m N ), then (I₁₀+10 I₉ ) is equal to -

Options

  1. A( e ¹⁰ )
  2. B( e ¹⁰ 10 )
  3. C( e )
  4. D( e -1 )

Correct answer

C. ( e )

Step-by-step solution

( aligned & I ₁₀= ₁^ e 1 ( x )¹⁰ dx = [( x )¹⁰ x ]₁^ e & - ₁^ e 10( x )^9 1 x xdx = e -0-10 ₁^ e ( x )^9 dx & = e -10 I ₉+10 I ₉= e aligned )

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