First slide

Methods of integration

Question

$if 2 < x < 3 \int (| x - 1 | | x - 2 | + | x - 3 |) d x$

Moderate

A

$- \frac{x^{2}}{2} + c$
B

$x + c$
C

$\frac{x^{2}}{2} + c$
D

$- x + c$

Solution

$\int [|x - 1| + |x - 2|] + |x - 3| d x$
$\begin{array}{l} If 2 < x < 3 \Rightarrow x - 1 > 0, x - 2 > 0, x - 3 < 0 \\ \int [x - 1 + x - 2 - (x - 3)] d x = \int x d x \end{array}$

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