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AP EAMCET202017 Sep 2020Evening ShiftMathematicsDefinite IntegrationActual

( ₀^1 ⁻¹ ( 2 x 1+x^2 ) d x= )

Options

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

Correct answer

C. ( 2 - 2 )

Step-by-step solution

(I= ₀^1 ⁻¹ ( 2 x 1+x^2 ) d x ) When, (x= , ) ( 2 x 1+x^2 = 2 1+ ^2 = 2 ) Also, ( d x= ^2 d ) and, When (x=0, =0 ) When (x=1, = 4 ) So, ( aligned I & = ₀^ / 4 ⁻¹( 2 ) ^2 d & = ₀^ / 4 2 ^2 d =2 ₀^ / 4 ^2 d aligned ) By parts we get, (I=2[ , - ]₀^ / 4 I= 2 - 2 )

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