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Question
Evaluate:
`∫_1^4|x - 2|dx`.
Sum
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Solution
Given:
`∫_1^4|x − 2|dx`.
`∫_1^2|x − 2|dx + ∫_2^4|x − 2| dx`
= `− ∫_1^2(x − 2)dx + ∫_2^4 (x-2}dx`
= `− [x^2/2 − 2x]_1^2 + [x^2/2 − 2x]_2^4`
= `− {(4/2 − 4) − (1/2 − 2)} + {(16/2 − 8) − (4/2 − 4)}`
= `{(−2) − (−3/2)} + {0 − (−2)}`
= `− (−2 + 3/2) + 2`
= `− (−1/2) + 2`
= `5/2`
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