First slide

Evaluation of definite integrals

Question

$\int_{0}^{2} |2 x - 1| d x$

Moderate

A

$\frac{3}{2}$
B

$\frac{7}{2}$
C

$\frac{5}{2}$
D

$\frac{9}{2}$

Solution

$\begin{array}{l} use definition of absolute value \\ | 2 x - 1 | \{\begin{cases} - (2 x - 1), & x < \frac{1}{2} \\ 2 x - 1, & x \geq \frac{1}{2} \end{cases} \\ ∴ \int_{0}^{2} | 2 x - 1 | d x = \int_{0}^{1 / 2} {- (2 x - 1)} d x + \int_{i / 2}^{2} (2 x - 1) d x \\ = {(x - x^{2})}_{0}^{1 / 2} + (x - x)_{1 / 2}^{2} \\ = \frac{5}{2} \end{array}$

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