Evaluate ∫_0 ^1 2^(x ) dx


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Question Number 192452 by Spillover last updated on 18/May/23

$E v a l u a t e \int_{0}^{1} 2^{x} d x$
	Answered by senestro last updated on 18/May/23

	$1 / \ln 2$
	Commented by Spillover last updated on 18/May/23

	$s h o w y o u r s o l u t i o n$
	Answered by manxsol last updated on 19/May/23

	$y = 2^{x}$ $l n y = x l n 2$ $\frac{d y}{y} = l n 2 d x$ $x = 0 y = 1$ $x = 1 y = 2$ $\int_{1}^{2} y \frac{d y}{y l n 2} = \frac{y}{l n 2} ∣_{1}^{2} = \frac{2}{l n 2} - \frac{1}{l n 2} = \frac{1}{l n 2}$
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