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Area and Volume Formulas

Area and Volume Formulas - rea and Volume Formulas In this...

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rea and Volume Formulas In this section we will derive the formulas used to get the area between two curves and the volume of a solid of revolution. Area Between Two Curves We will start with the formula for determining the area between and on the interval [ a,b ]. We will also assume that on [ a,b ]. We will now proceed much as we did when we looked that the Area Problem in the Integrals Chapter. We will first divide up the interval into n equal subintervals each with length, Next, pick a point in each subinterval, , and we can then use rectangles on each interval as follows. The height of each of these rectangles is given by, and the area of each rectangle is then,
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So, the area between the two curves is then approximated by, The exact area is, Now, recalling the definition of the definite integral this is nothing more than, The formula above will work provided the two functions are in the form and . However, not all functions are in that form. Sometimes we will be forced to work with functions in the form
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