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If f(x)={(e^(cosx)sinx, |x|le2),(2, othe...

If `f(x)={(e^(cosx)sinx, |x|le2),(2, otherwise):}` then `int_-2^3f(x)dx=` (A) `0` (B) `1` (C) `2` (D) `3`

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
C
Given , ` f (x) ={{:(e^(cos),sin x_(,),"for"|x|le2),(2,_(,),"otherwise"):}`
`:.int_(-2)^(3)f(x)dx=int_(-2)^(2)f(x)dx+int_(2)^(3)f(x)dx`
`=int_(-2)^(2)e^(cosx)sinxdx+int_(2)^(3)2 dx=0+2[x]_(2)^(3)`
`[:'e^(cosx)sinx " is an odd function "]`
`=2[3-2]=2` " " `[:'int_(-2)^(3)f(x)dx=2]`
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