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Manipal MET2015MathematicsDefinite Integration

The value of _ 2 ^ 3 x x^2 x^2+ ( 6-x^2 ) d x is

Options

  1. A1 4 3 2
  2. B1 2 3 2
  3. C3 2
  4. D1 6 3 2

Correct answer

A. 1 4 3 2

Step-by-step solution

Let I= _ 2 ^ 3 x x^2 x^2+ ( 6-x^2 ) d x Putting x^2=t 2 x d x=d t I= 1 2 _ 2 ^ 3 t t+ ( 6-t) d t ...(i) Using _a^b f(x) d x= _a^b f(a+b-x) d x , we get I= 1 2 _ 2 ^ 3 ( 6-t) ( 6-t)+ t d t ...(ii) On adding Eqs.(i) and (ii), we get 2 I= _ 2 ^ 3 1 d t=[t]_ 2 ^ 3 array ll & 2 I= 1 2 ( 3- 2)= 1 2 ( 3 2 ) & I= 1 4 ( 3 2 ) array

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