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

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

In general, the area enclosed by the curve \(y=\mathrm{f}(x)\), the \(x\)-axis, the lines \(x=a\) and \(x=b\), where \(a < b\), is given by

\({\displaystyle\displaystyle \displaystyle\int_{a}^{b} \mathrm{f}(x) \mathrm{d}x}\) when curve is above the \({x}\)-axis.

\( \left| \displaystyle \displaystyle \displaystyle\int_{a}^{b} \mathrm{f}(x) \mathrm{d}x \right| \) when curve is below the \({x}\)-axis.

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

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