First slide

Introduction to integration

Question

$\int | x | dx is equal to$

Easy

A

$\frac{1}{2} x^{2} + C$
B

$- \frac{x^{2}}{2} + C$
C

$x | x | + C$
D

$\frac{1}{2} x | x | + C$

Solution

$\begin{array}{l} Let I = \int | x | \cdot 1 dx = | x | x - \int \frac{| x |}{x} xdx = x | x | - \int | x | dx \\ \Rightarrow 2 I = x | x | \Rightarrow I = \frac{x | x |}{2} + C \end{array}$

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