Thread: Volume of rotation (y-axis)

The function is y(x) = 7/(x^2 +5x +6) evaluated from x = 0 to x = 1. Obviously it cannot be written as x(y). I tried changing the bounds of integration (from x values to their corresponding y values on the function), but this didn't work.

How do you do this? Please explain this in steps. Thanks!

Originally Posted by iheartmath

The function is y(x) = 7/(x^2 +5x +6) evaluated from x = 0 to x = 1. Obviously it cannot be written as x(y). I tried changing the bounds of integration (from x values to their corresponding y values on the function), but this didn't work.

How do you do this? Please explain this in steps. Thanks!

You can split the denominator into partial fractions using





which gives

A+B=0
2A+3B=1

Simply solve for A and B.

Then you can develop the volume of revolution using shells.

Originally Posted by iheartmath

The function is y(x) = 7/(x^2 +5x +6) evaluated from x = 0 to x = 1. Obviously it cannot be written as x(y). I tried changing the bounds of integration (from x values to their corresponding y values on the function), but this didn't work.

How do you do this? Please explain this in steps. Thanks!

rotating about the y-axis, using the method of cylindrical shells ...



partial fractions ...