I need to find the volume of the solid that is formed when the (x>0, y< -1) region of the curve y= -1/x is rotated about the y-axis.
If I'm correct, this volume can be calculated by: Evaluating the definite integral (upper bound = -1, lower bound = -infinity) of π*(1/y²) with respect to y.
In evaluating this integral, I got up to: Volume = (-π/1) - (-π/infinity) = -π
But how can a volume be a negative value? Please let me know if I've done anything wrong, and explain how to get the correct answer if you can.
Thank you x