Feb 28, 2026 · I have an integral, $$ I = \int_a^b x f (x) dx $$ and I would like to express this in terms of $\int_a^b f (x) dx$ if possible, but I don't see how integration by parts will help here.

Answers to the question of the integral of $\frac {1} {x}$ are all based on an implicit assumption that the upper and lower limits of the integral are both positive real numbers.

Feb 17, 2025 · The noun phrase "improper integral" written as $$ \int_a^\infty f (x) \, dx $$ is well defined. If the appropriate limit exists, we attach the property "convergent" to that expression and use …

Feb 6, 2026 · Evaluate an integral involving a series and product in the denominator Ask Question Asked 1 month ago Modified 1 month ago

The integral which you describe has no closed form which is to say that it cannot be expressed in elementary functions. For example, you can express $\int x^2 \mathrm {d}x$ in elementary functions …

If by integral you mean the cumulative distribution function $\Phi (x)$ mentioned in the comments by the OP, then your assertion is incorrect.

Feb 4, 2018 · The integral of 0 is C, because the derivative of C is zero. Also, it makes sense logically if you recall the fact that the derivative of the function is the function's slope, because any function f …

May 28, 2021 · I am having difficulties to compute this integral $$ \int_ {-\infty}^\infty e^ {\pm ix^2} \, dx. $$ I tried to use complex integration and Cauchy's theorem but it didn't work. Can someone help me?

Dec 15, 2017 · A different type of integral, if you want to call it an integral, is a "path integral". These are actually defined by a "normal" integral (such as a Riemann integral), but path integrals do not seek to …

Oct 11, 2025 · However, one "intrinsic integral closure" that is often used is the normalization, which in the case on an integral domain is the integral closure in its field of fractions. It's the maximal integral …