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MermaidWonders said:Ah, so is it like we're not supposed to do the "by comparison" for integrals, especially when we don't know whether the integral will be equal to infinity or not? I mean, why didn't she just circle the "converges as well" part?
... the only candidate is ln|x|...
Country Boy said:You error is that the "comparison test" applies only to positive functions.
tkhunny said:Well, BOTH positive, sure, but also BOTH negative would do.
Integral calculus is a branch of mathematics that deals with the calculation and properties of integrals, which are mathematical objects that represent the area under a curve.
The main difference between integral calculus and differential calculus is that integral calculus deals with the accumulation of quantities, while differential calculus deals with the rates at which quantities change.
Integral calculus is used in various fields such as physics, engineering, economics, and statistics to solve problems involving continuous change and accumulation. It is used to calculate areas, volumes, and other quantities that cannot be easily calculated by basic arithmetic operations.
Some common errors in integral calculus include forgetting to include the constant of integration, making algebraic mistakes, and using the wrong variable for integration. It is important to carefully check each step of the problem to avoid these errors.
To improve your skills in integral calculus, practice is key. Make sure you understand the basic concepts and techniques, and then solve a variety of problems to reinforce your understanding. You can also seek help from a tutor or online resources for additional practice and guidance.