Question

By using the properties of definite integrals, evaluate the following integral:
$integral subscript 2 superscript 5 open vertical bar straight x minus 1 close vertical bar dx$

Solution

Let I = $integral subscript 2 superscript 5 open vertical bar straight x minus 1 close vertical bar space dx$
For $2 less or equal than straight x less or equal than 5 comma space space straight x minus 1 greater than 0 space space space space space space rightwards double arrow space space space open vertical bar straight x minus 1 close vertical bar space equals space straight x minus 1$
$therefore space space space space space straight I space equals space integral subscript 2 superscript 5 left parenthesis straight x minus 1 right parenthesis space dx space equals space open square brackets straight x squared over 2 minus straight x close square brackets subscript 2 superscript 5 space equals space open parentheses 25 over 2 minus 5 close parentheses minus left parenthesis 0 minus 0 right parenthesis space equals space 15 over 2$

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Integrals

By using the properties of definite integrals, evaluate the following integral:
$integral subscript 2 superscript 5 open vertical bar straight x minus 1 close vertical bar dx$

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