Problems Involving Integration Please

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A student in their second semester of physics seeks resources for practice problems that involve calculus, particularly integration, as their coursework heavily emphasizes this skill. They express confidence in solving difficult problems but struggle with those requiring calculus, exemplified by a test question about a string with variable linear mass density. The student understands the basic concepts but gets stuck when applying them to more complex scenarios. They request recommendations for textbooks or websites that provide calculus-based physics problems. The discussion highlights the need for targeted practice in integrating calculus with physics concepts.
SpeeDFX
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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 textbook, 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
 
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please someone assist me :)
 
Why not google on "calculus problems physics", and see if anything there is of use ?
 

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