l'Hôpital said:Let u^2 = x
jrlaguna said:It's just there, the arc tangent.
D H said:You looked up the indefinite integral. You have a definite integral. Apply the integration limits.
An analytic solution is a solution to a mathematical problem that can be obtained through a series of logical steps, usually by using equations and formulas. It is a precise and exact solution, as opposed to a numerical solution which is an approximation.
An analytic solution is exact and obtained through mathematical equations and formulas, while a numerical solution is an approximation obtained through a series of calculations with a finite number of steps. Analytic solutions are often preferred because they provide a deeper understanding of the problem at hand.
An analytic solution is used when a mathematical problem can be solved through a series of logical steps and equations. It is commonly used in physics, engineering, and other scientific fields to solve problems related to motion, heat transfer, and other physical phenomena.
Using an analytic solution allows for a more precise and exact solution to a mathematical problem. It also provides a deeper understanding of the problem and allows for the derivation of other related equations and formulas. Additionally, it can often be more efficient and faster to obtain an analytic solution compared to a numerical solution.
No, not all problems can have an analytic solution. Some problems are too complex or do not have a known mathematical solution. In these cases, a numerical solution may be used to approximate the solution. Additionally, some problems may have analytic solutions, but they may be too difficult or time-consuming to obtain, in which case a numerical solution may be preferred.