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int(-2)^0{x^3+3x^2+3x+3+(x+1)cos(x+1)dxi...

`int_(-2)^0{x^3+3x^2+3x+3+(x+1)cos(x+1)dxi se q u a lto` `-4` (b) 0 (c) 4 (d) 6

A

0

B

3

C

4

D

1

Text Solution

Verified by Experts

The correct Answer is:
C
Let `I=int_(-2)^(0)[x^(3)+3x^(2)+3x+3+(x+1)cos(x+1)]dx`
`=int_(-2)^(0)[(x+1)^(3)+2+(x+1)cos(x+1)]dx`
Put x+1 =t
`rArrdx = dt`
`:. I=int_(-1)^(1)(t^(3)+2+tcost)dt`
`=int_(-1)^(1)t^(3)dt+2int_(-1)^(1)dt+int_(-1)^(1)tcost dt`
`=0+2*3[x]_(0)^(1)+0 =4 `
[ since , `t^(3)` and t cos t are odd functions]
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