1.

` int_(-1)^(2)f(x)dx " where " f(x) = |x+1| +|x|+ |x-1|` is equal toA. `7/2`B. `9/2`C. `13/2`D. `19/2`

Answer» Correct Answer - D
We can redefine f as f as `f (x) = {:{(2-x,"if"-1 lt x le 0),(x+2,"if " 0 lt x le 1 ),(3x,"if " 1ltxle 2):}`
Therefore,
` int_(-1)^(2) f(x) dx = int_(-1)^(0) (2-x) dx + int _(0)^(1) (x+2) dx + int_(1)^(2)3x dx`
` = [ 2x - (x^(2))/2]_(1)^(0)+[ (x^(2))/2+2x] _(0)^(1) + [ (3x^(2))/2]_(1)^(2)`
` = { 0- (-2-1/2)}+(1/2 +2 )+3 (4/2-1/2)= 5/2 +5/2 +9/2 = 19/2 `


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