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Question
Evaluate the following : `int_(-2)^(3) |x - 2|*dx`
Sum
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Solution
|x – 2| = 2 – x, if x < 2
= x – 2, if x ≥ 2
∴ `int_(-2)^(3) |x - 2|*dx = int_(-2)^(3) |x - 2|*dx + int_(2)^(3)|x - 2|*dx`
= `int_(-2)^(3) (2 - x)*dx + int_(2)^(3) (x - 2)*dx`
= `[(2 - x)^2/((- 2))]_(-2)^(2) + [(x - 2)^2/2]_3^2`
= `[0 - (4)^2/(- 2)^2] + [1^2/2 - 0^2/2]`
= `8 + (1)/(2)`
= `(17)/(2)`.
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