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AP EAMCET202318 May 2023Evening ShiftMathematicsDefinite IntegrationActual

If I = ₁^3 3+ x + x ^2 dx , then I lies in the interval

Options

  1. A(2 5 , 2 15 )
  2. B( 3 , 2 5 )
  3. C( 23 , 33 )
  4. D(2 15 , 23 )

Correct answer

A. (2 5 , 2 15 )

Step-by-step solution

I = ₁^3 3+ x + x ^2 dx = ₁^3 ( x + 1 2 )^2+ ( 11 2 )^2 dx gathered = [ (x+ 1 2 ) 2 x^2+x+3 + 11 4 2 (x+ 1 2 )+ x^2+x+3 ]₁^3 = [ 7 4 15 + 11 8 | 7 2 + 15 |- 3 4 5 - 11 8 | 3 2 + 5 | ] = 1 4 [7 15 -3 5 ]+ 11 8 [ ( 7+2 15 3+2 5 ) ] = 5 4 [7 3 -3]+ 11 8 [ 7+2 15 3+2 5 ] =5.100066+0.9344 I-6.0344 (2 5 , 2 15 ) gathered

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