arc length y=2x^2+3, 0<= x<= 1

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

simplify solve for inverse tangent line

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arc length y=2x²+3, 0≤ x≤ 1

Solution

14 (2√17+12 ln(4+√17))

Decimal

2.32339…

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Arc length of a function definition

The arc length of a function is the length of a curve f(x) on an interval [a, b] given by
L=∫_a^b√1+(f ′(x))²dx

Apply the arc length formula: ∫₀¹√1+16x²dx

Solve ∫₀¹√1+16x²dx: 14 (2√17+12 ln(4+√17))

The arc length is:

=14 (2√17+12 ln(4+√17))

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

arc length y=2x^2+3, 0<= x<= 1

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