What is the washer method formula?

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Karbamidjts · Accepted Answer

For the Washer MethodThe area of a disk is the area of a circle.  The volume is the area       π          r      2       times the thickness, which will be either dx or dy depending on the problem. Thus, it will be either       π          r      2              d      x       or       π          r      2              d      y      Thus, for some a and b, we&#039;ll have                     ∫        a        b                    (      π              R        2            -      π              r        2            )        d          x or dy      Where R is the radius of the larger disk and r that of the smaller.The radii functions must have the same independent variable as the differential.If revolving around a horizontal line       y    =    k  , the thickness of the representative disk will be the differential dx.In this case:The larger disk will be determined by the function       y    =          g              (        x        )             farther from the line       y    =    k   and the smaller disk, by the function       y    =          f              (        x        )             closer to       y    =    k  If revolving around a vertical line       x    =    h  , the thickness of the representative disk will be the differential dy.In this case:The larger disk will be determined by the function       x    =          g              (        y        )             farther from the line       x    =    h   and the smaller disk, by the function       x    =          f              (        y        )             closer to       x    =    h  It must be taken into account if the graphs of the functions cross each other of the line about which we are rotating.If a region must be divided into two or more parts, the volume must be calculated using two or more integrals.

What is the washer method formula?

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