6.1 Areas Between Curves/20: Difference between revisions
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<math> | <math> | ||
4x+y^2=12, x=y | 4x+y^2=12, x=y | ||
</math> | </math> | ||
<math> | <math> | ||
4x | \frac{4x}{4}=\frac{-y^2+12}{4} | ||
</math> | |||
<math> | |||
x=-\frac{1}{4}y^2+3 | |||
</math> | |||
<math> | |||
\int_{0}^{3}(-\frac{1}{4}y^2-y+3)-y | |||
</math> | |||
<math> | |||
\int_{0}^{3} -\frac{1}{4}y^2-y+3 | |||
</math> | |||
<math> | |||
\frac{\frac{1}{4}y^3}{3}-\frac{y^2}{2}+3y | |||
</math> | |||
<math> | |||
-\frac{1}{12}y^3-\frac{1}{2}y^2+3y\bigg|_{0}^{3} | |||
</math> | |||
<math> | |||
-\frac{1}{12}(3)^3-\frac{1}{2}(3)^2+3(3) | |||
</math> | |||
<math> | |||
=2.25 | |||
</math> | |||
Revision as of 20:15, 12 October 2022
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 4x+y^2=12, x=y }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \frac{4x}{4}=\frac{-y^2+12}{4} }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle x=-\frac{1}{4}y^2+3 }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \int_{0}^{3}(-\frac{1}{4}y^2-y+3)-y }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \int_{0}^{3} -\frac{1}{4}y^2-y+3 }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \frac{\frac{1}{4}y^3}{3}-\frac{y^2}{2}+3y }
Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle -{\frac {1}{12}}y^{3}-{\frac {1}{2}}y^{2}+3y{\bigg |}_{0}^{3}}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle -\frac{1}{12}(3)^3-\frac{1}{2}(3)^2+3(3) }
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle =2.25 }