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AP EAMCET2015MathematicsDefinite Integration

₀^ 4 x+ x 3+ 2 x d x is equal to

Options

  1. A1 2 3
  2. B2
  3. C3
  4. D1 4 3

Correct answer

D. 1 4 3

Step-by-step solution

Let I= ₀^ / 4 x+ x 3+ 2 x d x Put x- x=t( x+ x) d x=d t Limits: aligned & x=0 & t= - =-1 & x= 4 t= 4 - 4 =0 & 2 x=1-1+ 2 x & =1-(1- 2 x) & =1- ( ^2 x+ ^2 x-2 x x ) & =1-( x- x)^2 & =1-t^2 aligned Now, I= _ -1 ^0 d t 3+1-t^2 = _ -1 ^0 d t (2)^2-(t)^2 aligned & = 1 4 [ ( 2+t 2-t ) ]_ -1 ^0 & =- 1 4 1 3 = 1 4 3 aligned

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