Let I1=int(-2)^2 (x^6+3x^5+7x^4)/(x^4+2)...

Let `I_1=int_(-2)^2 (x^6+3x^5+7x^4)/(x^4+2)dx` and `I_2=int_(-3)^1 (2(x+1)^2+11(x+1)+14)/((x+1)^4+2)dt`. Then the value of `I_1+I_2` is (a)8 (b) `(200)/3` (c) `(100)/3` (d) none of these

`8`

`200//3`

`100//3`

noe

Text Solution

Verified by Experts

The correct Answer is:

In `I_(2)` put `x+1=t`. Then
`I_(2)=int_(-2)^(2)(2t^(2)+11t+14)/(t^(4)+2)dt=int_(-2)^(2)(2x^(2)+11x+14)/(x^(4)+2)dx`
`:. I_(1)+I_(2)=int_(-1)^(2)(x^(6)+3x^(5)+7x^(4)+2x^(2)+11x+14)/(x^(4)+2) dx`
`int_(-2)^(2)((x^(2)+3x+7)(x^(4)+2)+5x)/(x^(4)+2)dx`
`=int_(-2)^(2)(x^(2)+3x+7)dx+5int_(-2)^(2)x/(x^(4)+2)dx`
`=2 int_(0)^(2)(x^(2)+7)dx=100/3`

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