First slide

Evaluation of definite integrals

Question

$\int_{0}^{2 π} [2 \sin x] d x =$

Moderate

A

$- \frac{5 π}{3}$
B

$- π$
C

$\frac{5 π}{3}$
D

$- 2 π$

Solution

$I = \int_{0}^{\frac{π}{6}} 0. d x + \int_{\frac{π}{6}}^{\frac{5 π}{6}} 1. d x + \int_{\frac{5 π}{6}}^{π} 0. d x + \int_{π}^{\frac{7 π}{6}} (- 1) d x + \int_{\frac{7 π}{6}}^{\frac{11 π}{6}} (- 2) d x + \int_{\frac{11 π}{6}}^{2 π} (- 1) d x$
$= \frac{4 π}{6} - \frac{π}{6} - \frac{8 π}{6} - \frac{π}{6} = - π$

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