Problems Involving Integration Please...
Hi, I'm taking my second semester of physics right now. I do a lot of practice problems from my book and am able to complete the problems marked "difficult" without much trouble. Even though these problems are a little more challenging, they hardly ever employ the use of calculus (integration), which is something my teacher loves to play with. I'm looking for a text book, web site, or any other source that has physics problems that require the use of calculus to solve. I NEEEEEED to practice this, because these problems get me EVERY time.
An example of a problem that my teacher gave my class recently on a test is the following...
"a string hangs from the ceiling. It has a variable linear mass density that is zero at the bottom of the string and increases linearly until it reaches a maximum value at the top. The string has mass M and length L." Find the linear mass density and the speed of transverse wave along this string.
I understood in the case of a string with a constant linear mass density, the speed of a wave will increase as it nears the top of the string, and since in that case the string had a linear mass density that increased towards the top, the same behaviour would be exaggurated (for the lack of a better word). I knew the equation for the speed of a wave along a string, and I know the the linear mass density would some kind of function of x, but I got stuck there and had no idea how to proceed.
Problems like THAT are what i'm looking for. Any help is appreciated