Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

$https://latex.codecogs.com/png.image?\large \dpi{110}\int_{0}^{\frac{\pi}{6}}\: \sin 2x\: dx$ is gelijk aan	A.
	B.
	C.
	D.
	E.

[ 6-1951 - op net sinds 5.4.13-(E)-3.11.2023 ]

Translation in E N G L I S H

$https://latex.codecogs.com/png.image?\large \dpi{110}\int_{0}^{\frac{\pi}{6}}\: \sin 2x\: dx$ is equal to	A.
	B.
	C.
	D.
	E.

Oplossing - Solution

$https://latex.codecogs.com/png.image?\dpi{110}\int_{0}^{\frac{\pi}{6}}\sin 2x\: dx=\frac 12 \int_{0}^{\frac{\pi}{6}}\sin 2x\: d(2x)=\frac 12 \left [ -\cos 2x \right ]_{0}^{\frac{\pi}{6}}\\= \frac 12\left [ -\cos \frac{\pi }{3}-(-\cos 0) \right ]=\frac 12\left [ -\frac 12+1 \right ]=\frac 12\cdot \frac 12=\frac 14$