How to do integration by parts and which functions to choose.

The arc length formula is very useful. When we are trying to compute the length of some segment of Or A part or a section of some function, We would use it later when we have to deal with engineering problem. The formula is based on the integral between A and B of the square root of 1 plus F Prime squared DX, We can prove this formula using the fundamental theorem of calculus. We can use it to find the parameter of the circle, The length of any segment, and we can use it to find more concerning engineer problems. Like, the length of a cable length of any shape that we want to use in some engineering problem. The length formula is very useful. When we are dealing with calculus problems later, we can use it when we try to find the volume of some shapes. Using the lateral surface area. This formula is great. It can be proved by the mean value theorem by adding the sums of the sections that we can integrate.
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In using integration bypart. Sometimes We don't know which Function to choose to integrate first. We know that the integration bypass, let us choose between two functions, F and T, we have to choose. Which one is the first derivative? And which one is the second derivative And how to combine them to get to change the function and make it easier to compute using integration by a part? We can let f equal F. Prime and G is the integration of G And combine in the integration and differentiation. We can get the result that we need. We can use substitution as well or we can use a change of variable. This is this work sometime And we can use the sign and the cosine, or maybe the tangent to combine both, or all these to find the function that we need By the end. Doing a change of variable or an integration bypass or any kind of substitution will help us find the Primitive that we look for the fundamental theorem of calculus that has find the derivative. And from there, we see if the function is increasing or decreasing. Sometimes we are interested in Computing, the second derivative. And we want to see if the function is concave up or concave down, and that's what we need to do.
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