Disk Method Around Y Axis Math

It really depends on the situation you have. Disc method around y axis. Take y x 2 but this time using the y axis between y 0 4 and y 1 4.

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Calculating integral disc around vertical line.

Disk method around y axis math. Disc washer methods challenge. Revolving around x or y axis. Wow that was easy. Rotate the region between the curve and the y axis around the y axis and ﬁnd the volume of the resulting solid.

Find volumes of solids of revolution around any horizontal or vertical line using the disc method. The difference is that the radius becomes different but the same sort of discs are created inside of the figure. Volume with disc method. Using theorem 6 2 v p z b a f x 2 dx z 1 0 2 2 px5 5 1 0 p 5.

This is the currently selected item. This is the currently selected item. Rotate it around the y axis. Revolving around x or y axis.

Let y f x 2 on the interval 0 1. So we want something like x g y instead of y f x. Revolving around x or y axis. If you have a function y f x and you rotate it about the x axis you should use disk or ring same thing in my mind.

We know that the center of our disk will always have a y coordinate of 0 because we rotated our function around the line mathbf y 0. Math ap college. Volume with washer method. If you rotate y f x about the y axis you should use shell.

And we will leave the x coordinate as the variable x because we are trying to find the volume of any disk along this figure with all different x values not just the one disk drawn above. This is basically the same thing as letting y x 2 1 rotate around the y axis but instead we rotated it around a line that is parallel to it in this case x 2. Math ap college calculus ab applications of integration volume with disc method. X y now integrate pi times the square of y 2 and dx is now dy.

And now we want to integrate in the y direction. Revolving around x or y axis. Of course you can always use both methods if you can find the inverse of the function. In this case it is.

Revolving around x or y axis. Curve y x2 rotated about the x axis.