Wiskunde Multiple Choice Vraag uit Gricha's Wiskundige Vragenbank

De onbepaalde integraal $https://latex.codecogs.com/png.image?\dpi{110}\int \frac{45}{\sqrt{4-5x}}\: dx$ is gelijk aan	A. \(\boldsymbol{-\,18\sqrt {4-5x} +C}\)
	B. \(\boldsymbol{-\,\frac {2} {9}\sqrt{4-5x} +C}\)
	C. \(\boldsymbol{9\sqrt {4-5x} +C}\)
	D. \(\boldsymbol{90\sqrt {4-5x} +C}\)
	E. \(\boldsymbol{\text {geen van de vorige} }\)

[ 6-3493 - op net sinds 3.8.08-()-15.6.2024 ]

Translation in E N G L I S H

$https://latex.codecogs.com/png.image?\dpi{110}\int \frac{45}{\sqrt{4-5x}}\: dx$	A. \(\boldsymbol{-\,18\sqrt {4-5x} +C}\)
	B. \(\boldsymbol{-\,\frac {2} {9}\sqrt{4-5x} +C}\)
	C. \(\boldsymbol{9\sqrt {4-5x} +C}\)
	D. \(\boldsymbol{90\sqrt {4-5x} +C}\)
	E. \(\boldsymbol{\text {none of these} }\)

Oplossing - Solution

$\\ \int \frac{45}{\sqrt{4-5x}}\: dx=\frac{45}{-5}\int \frac{1}{\sqrt{4-5x}}\: d(4-5x) \\ \quad =-9\cdot (2\sqrt{4-5x})+C=-18\sqrt{4-5x}+C$

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