An Example Application of the Integrals

We reprodnce here some nsefnl formnlae for the determination of area under the cnrve, the arc length, volnme of solid revolntion, and the snrface area that are the results of the application of the integrals. Let fix) be a real valned fnnction dehned on an interval (a,b). Let A be the area bonnded by the fnnction, the x-axis, and the lines x = a and x = b. Then 

The volume of the solid generated by revolving the curve fix) about the x-axis is 

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