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If f(x)={1-|x|,|x|lt=1 0,|x|>1'a n dg(x)...

If `f(x)={1-|x|,|x|lt=1 0,|x|>1'a n dg(x)=f(x-1)+f(x+1),` find the value of `int_(-3)^3g(x)dxdot`

Text Solution

Verified by Experts

The correct Answer is:
2

Graph of `y=f(x-1)`
`int_(-3)^(3)g(x)dx=int_(-3)^(3)f(x-1)dx+int_(-3)^(3)f(x-1)dx`
`=` Area of triangle in the graph `y=f(x-1)`
`+` Area of triangle in the graph `y=f(x+1)`
`=2 1/2 (2)(1)=2`
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