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Let f(x)={(1-|x|","|x|le1),(0","|x|gt1):...

Let `f(x)={(1-|x|","|x|le1),(0","|x|gt1):} and g(x)=f(x-1)"for all" x in R` The value of ` int_(-3)^(3) g (x) dx ` is

A

2

B

3

C

4

D

5

Text Solution

Verified by Experts

The correct Answer is:
A
The graph of f(x) and g(x) are shown in Fig. 14 and 15 respectively.

Clearly,
`overset(3)underset(-3)int g(x)dx=overset(-2)underset(-3)int 0 dx+overset(0)underset(-2)int f(x)dx+overset(2)underset(0)intf(x)dx+overset(3)underset(2)int 0 dx`
`rArr overset(3)underset(-3)intg(x) dx=2overset(2)underset(0)int f(x) dx=2((1)/(2)xx2xx1)=2`
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