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If f(x)={{:(e^(cosx), sin x, "for" |x|le...

If `f(x)={{:(e^(cosx), sin x, "for" |x|le2),(,2,"otherwise"):}` then `int_(-2)^(3)f(x)dx`=

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`I=underset(-2)overset(3)intf(x)dxunderset(-2)overset(3)int e^(cosx) sin x dx + underset(2)overset(3)int 2 dx`
`rArr I=0+2(3-2)[ {:( :., g(x) =e^(cosx) "sin x is an odd function"),( :., underset(-2)overset(2)int (x) dx=0):}]`
`rArr I=2`
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