6.1 Areas Between Curves/13 - Revision history

Elizabethh58413 at 20:12, 20 September 2022

2022-09-20T20:12:40Z

← Older revision		Revision as of 20:12, 20 September 2022
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	<math>\color{blue}{y=x^2-6}</math>		<math>\color{blue}{y=x^2-6}</math>

			[[File:Screen Shot 2022-09-20 at 1.07.09 PM.png\|right\|500px]]

	<math>\int_{-3}^{3} \left\|(12-x^2) - (x^2-6) \right\| dx </math>		<math>\int_{-3}^{3} \left\|(12-x^2) - (x^2-6) \right\| dx </math>

2022-09-20T20:05:45Z

← Older revision		Revision as of 20:05, 20 September 2022
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	<math>		<math>
	\begin{align}		\begin{align}
	\int_{-3}^{3} \left\|(12-x^2) - (x^2-6) \right\| dx &= (12x-\frac{1}{3}x^3) - (\frac{1}{3}x^3 - 6x) \Bigg\|_{-3}^{3} \\		\int_{-3}^{3} \left\|(12-x^2) - (x^2-6) \right\| dx &= [(12x-\frac{1}{3}x^3) - (\frac{1}{3}x^3 - 6x)] \Bigg\|_{-3}^{3} \\
			& = [(12(3) - \frac{1}{3}(3)^3) - (\frac{1}{3}(3)^3-6(3) )] - [(12(-3) - \frac{1}{3}(-3)^3) - (\frac{1}{3}(-3)^3-6(-3) )] \\
	& = 36-(-36) \\		& = 36-(-36) \\
	& = 72		& = 72
	\end{align}		\end{align}
	</math>		</math>

2022-09-20T19:58:51Z

2022-09-20T19:58:20Z

← Older revision		Revision as of 19:58, 20 September 2022
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	<math>\color{blue}{y=x^2-6}</math>		<math>\color{blue}{y=x^2-6}</math>

	<math>\int_{3}^{-3} \left\|(12-x^2) - (x^2-6) \right\| dx </math>

			<math>\int_{-3}^{3} \left\|(12-x^2) - (x^2-6) \right\| dx </math>
			<math>
			\begin{align}
			12-x^2 &= x^2-6 \\
			18 &= 2x^2 \\
			9 &=x^2 \\
			\pm3 &= x
			\end{align}
			</math>

			<math>
			\begin{align}
			\int_{-3}^{3} \left\|(12-x^2) - (x^2-6) \right\| dx &= (12x-\frac{1}{3}x^3) - (\frac{1}{3}x^3 - 6x) \Bigg\|_{-3}^{3} \\
			& = 36-(-36) \\
			& = 72
			\end{align}
			</math>

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