Area of an ellipse (and volume of an elliptical cylinder) using calculus
We know the formula for an ellipse with half axes is
To find the area of one half of the ellipse, we integrate y from -a to a:
To find the area of the whole ellipse, we multiply the above by 2. Now we have the area of the base of our elliptic cylinder.
Compare this result with the area formula for an ellipse with half axes a and b:
Area = π*a*b. How close are the two answers?
Then to find the volume, we simply multiply our previous result (area of the base) by the height h of the elliptic cylinder.
