For $a

Question

For $a<b$, total area between $y=\mathrm f(x)$ and the $x$-axis is $A=\int_a^b|\mathrm f(x)|\,\mathrm dx$ Position of curvePositive area Above the $x$-axis Below the $x$-axis Split where the function changes sign and add positive areas. A touching zero with no sign change needs no split.

Accepted Answer

Above the $x$-axis: $A=\int_a^b \mathrm f(x)\,\mathrm dx$ Below the $x$-axis: $A=\left|\int_a^b \mathrm f(x)\,\mathrm dx\right|$

Position of curve	Positive area
Above the \(x\)-axis
Below the \(x\)-axis

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

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

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