7) Application of Integration to find areas under plane curves and volumes of Solids of revolution

• Integration can be used to find the area under a curve, which can represent the distance traveled by an object or the work done by a force.
• It can also be used to find the volume of a solid of revolution, which is formed by rotating a curve around an axis.

Important Formulas to Remember in these topic

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$$\text{Area } = \int_a^b f(x)dx$$

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$$\text{Volume } = \int_a^b \pi y^2 dx$$

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$$\text{Volume } = \int_a^b \pi R^2 dx$$

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