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Question
Evaluate: `int_(-1)^2 |x^3 - x| dx`
Evaluate
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Solution
`int_(-1)^2 |x^3 - x| dx = int_(-1)^0 (x^3 - x) dx - int_0^1 (x^3 - x) dx + int_1^2 (x^3 - x) dx`
= `[x^4/4 - x^2/2]_(-1)^0 - [x^4/4 - x^2/2]_0^1 + [x^4/4 - x^2/2]_1^2`
= `[(0 - 0) - (1/4 - 1/2)] - [(1/4 - 1/2) - (0 - 0)] + [(4 - 2) - (1/4 - 1/2)]`
= `1/4 + 1/4 + 2 + 1/4`
= `11/4`
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