Express the curve as $x=\mathrm g(y)$ and use $y$-limits, $a

Question

Express the curve as $x=\mathrm g(y)$ and use $y$-limits, $a<b$. $A=\int_a^b|\mathrm g(y)|\,\mathrm dy$ Position of curvePositive area Right of the $y$-axis Left of the $y$-axis Match the variable and limits Boundary axisIntegralLimits $x$-axis $y$-axis Split where $\mathrm g(y)$ changes sign. For two boundaries, integrate right minus left on each interval where their order is fixed.

Accepted Answer

Right of the $y$-axis: $A=\int_a^b \mathrm g(y)\,\mathrm dy$ Left of the $y$-axis: $A=\left|\int_a^b \mathrm g(y)\,\mathrm dy\right|$

Position of curve	Positive area
Right of the \(y\)-axis
Left of the \(y\)-axis

Boundary axis	Integral	Limits
\(x\)-axis
\(y\)-axis

Area Enclosed by the Curve and the \(y\)-axis

Area Enclosed by the Curve and the \(y\)-axis

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