I’m sure most of us have at least some experience with integrals being tricky and hard to compute. Whether it be trig substitution or some other method integrals can be very difficult. There are also functions, real functions that do not have an antiderivative, functions like:

$e^{-x^2}$ or $\frac{sin x}{x}$

However, there are ways to evaluate these integrals, and these are contained in the numerical methods. It is worth studying these methods one, to find the area under the cover for these certain functions, and two, to test the accuracy of these methods. There are certain methods in this chapter which my teammates will tell you more about.

Samuel CoskeyNumerical integration sounds hugely important to solving integrals (and equations) when abstract methods fail (as they seem to often)!

Means: there are ways to evaluate a

definiteintegral of these functions by approximations. As you said, you cannot evaluate them formally, and this makes it hard to find exact solutions!PS: don’t forget to categorize your post (I edited this one).

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