\displaystyle \textbf{1.}\ \text{Let }f(x)\text{ be a continuous function defined on }[a,b].\ \text{Then, the area bounded} \\ \text{by the curve }y=f(x),\text{ the }x\text{-axis and the ordinates }x=a\text{ and }x=b\text{ is given by }
\displaystyle \int_{a}^{b} f(x)\,dx\ \ \text{or,}\ \ \int_{a}^{b} y\,dx.

\displaystyle \textbf{2.}\ \text{If the curve }y=f(x)\text{ lies below the }x\text{-axis, then the area bounded by the curve} \\ y=f(x),\text{ the }x\text{-axis and the ordinates }x=a\text{ and }x=b\text{ is negative. So, the area is} \\ \text{given by }
\displaystyle \left|\int_{a}^{b} y\,dx\right|.

\displaystyle \textbf{3.}\ \text{The area bounded by the curve }x=f(y),\text{ the }y\text{-axis and the abscissae} \\ y=c\text{ and }y=d\text{ is given by }
\displaystyle \int_{c}^{d} f(y)\,dy\ \ \text{or,}\ \ \int_{c}^{d} x\,dy.

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