volume about x=-1, y=\sqrt[3]{x}, y=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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volume about x=−1, y=³√x, y=1

Solution

23π14

Decimal

5.16118…

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The volume for solid of revolution for a curve definition

The volume for solid of revolution for a curve is the volume of object determined by a curve f(y) rotated around x=d on an interval [a, b] given by
V=∫_a^bπ (f(y)−d)²dy

Apply the volume formula: ∫₀¹π(y³+1)²dy

Solve ∫₀¹π(y³+1)²dy: 23π14

The volume for solid of revolution is:

=23π14

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

volume about x=-1, y=\sqrt[3]{x}, y=1

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