Finals coming up and I am about ready to drop...

I feel, or rather felt, your pain. Like alot of this stuff, it's easier to say what the law means, than to apply it. My suggestion is to slowly  work through the examples in your book, and try to figure out each step. Is there a particular problem, or part of one, you can't figure out?

encyclopedia says:

in physics, a fundamental quantitative relationship between an electric current and the magnetic field it produces, based on the experiments in 1820 of the French scientists Jean-Baptiste Biot and Félix Savart.

An electric current flowing in a conductor, or a moving electric charge, produces a magnetic field, or a region in the space around the conductor in which magnetic forces may be detected. The value of the magnetic field at a point in the surrounding space may be considered the sum of all the contributions from each small element, or segment, of a current-carrying conductor. The Biot-Savart law states how the value of the magnetic field at a specific point in space from one short segment of current-carrying conductor depends on each factor that influences the field. In the first place, the value of the magnetic field at a point is directly proportional to both the value of the current in the conductor and the length of the current-carrying segment under consideration. The value of the field depends also on the orientation of the particular point with respect to the segment of current. If the line from the point to the short segment of current makes an angle of 90 with the current segment or lies straight out from it, the field is greatest. As this angle gets smaller, the field of the current segment diminishes, becoming zero when the point lies on a line of which the current element itself is a segment. In addition, the magnetic field at a point depends upon how far the point is from the current element. At twice the distance, the magnetic field is four times smaller, or the value of the magnetic field is inversely proportional to the square of the distance from the current element that produces it.

The Biot-Savart law is applied in a specific case by adding up the contributions to the magnetic field at a given point from the whole series of short current segments that constitute a specific conductor of whatever shape. For instance, with a very long straight wire carrying current, the value of the magnetic field at a point nearby is just directly proportional to the value of the current and inversely proportional to the perpendicular distance from the wire to the given point. Compare Ampère's law.

My book has jack in it. I am not sure about the calculus. What do I integrate? r from zero to max lenght?

If I can just get a 50% in the class I will pass!!!

What is the geometry? What exactly is the problem you're trying to solve?

I don't know the answer, but you might have better luck searching for it on Yahoo.

I thought he *was* asking the yahoos. . . . [:D]

well the integration depends on the size of the object..like if its  a sphere..or a cylinder..or a square..etc. You should be able to identify the shapes and memorize the formulas associated with it....be careful of outside forces too..oh man..i hated physics..even though im an electircal engineer...physics was a slut