A "signed definite integral" for computing work and other "net change" calculations. The value of an expression such as $\int_0^1 x^2\,dx$ comes out the same under all these interpretations, …

Jun 21, 2014 · 概念的话dx就是把定义域的x范围无限分（微分）其中的一份如x1 到x2 这一小段就是dx。 同理，dy就是值域的无限分为f (x2)-f (x1)。 dy/dx 是f (x)一个微分成dx dy围成的小三 …

The symbol used for integration, $\int$, is in fact just a stylized "S" for "sum"; The classical definition of the definite integral is $\int_a^b f (x) dx = \lim_ {\Delta x \to 0} \sum_ {x=a}^ {b} f …

May 2, 2015 · Okay this may sound stupid but I need a little help... What do $\\Large \\frac{d}{dx}$ and $\\Large \\frac{dy}{dx}$ mean? I need a thorough explanation. Thanks.

Dec 27, 2013 · $\\Delta x$, $\\delta x$ and $dx$ are used when talking about slopes and derivatives. But I don't know what the exact difference is between them.

These identities for $\int_0^1 x^ {-x}\ dx$ and $\int_0^1 x^x\ dx$ are sometimes called the "sophomore's dream". Look that up on Wikipedia.

I am working on trying to solve this problem: Prove: $\\int \\sin^n{x} \\ dx = -\\frac{1}{n} \\cos{x} \\cdot \\sin^{n - 1}{x} + \\frac{n - 1}{n} \\int \\sin^{n - 2}{x ...

Digital Transformation缩写可以写DT，也可以是DX，X通常会有交叉、横跨、转换的意思，同时还可以解读为数字化转型之后的不确定性、不可预测的X。

Oct 29, 2025 · The answer should be $ {I_n = \int_0^ {\pi} \frac {x \sin (nx)} {1 - \cos x}dx=\pi \left (n\ln4+1- (-1)^n-2n\sum_ {k=1}^ {n-1} \frac { (-1)^ {k-1}} {k}\right)}$. Am I right?

Here, $ (dx)^2$ means $dx \wedge dx$, and the fact that it vanishes comes from the fact that the exterior algebra is anti-commutative. In other words, formally we have $d^2x=0$ and $ …