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- calculus - Finding $\int x^xdx$ - Mathematics Stack Exchange
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
- What does $dx$ mean? - Mathematics Stack Exchange
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, of course In more general settings, the three interpretations generalize in different ways, so that the "dx" comes to mean different things
- What does the dx mean in an integral? [duplicate]
I know dy dx for example means "derivative of y with respect to x," but there's another context that confuses me You will generally just see a dx term sitting at the end of an integral equation an
- What do the symbols d dx and dy dx mean? - Mathematics Stack Exchange
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
- What is $dx$ in integration? - Mathematics Stack Exchange
The symbol used for integration, $\int$, is in fact just a stylized "S" for "sum"; The classical definition of the definite integral is $\int_a^b f (x) dx = \lim_ {\Delta x \to 0} \sum_ {x=a}^ {b} f (x)\Delta x$; the limit of the Riemann sum of f (x) between a and b as the increment of X approaches zero (and thus the number of rectangles approaches infinity)
- Integrating $\int \sin^n {x} \ dx$ - Mathematics Stack Exchange
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
- calculus - What is the true, formal meaning and reason for the dx . . .
But then others told me that "dx" is part of what's being integrated, and they started saying that we're led to believe that its just a delimiter in early courses because it'd be impossible for teachers to introduce "differentials," which is what things like dx and du are, so u-substitution isn't just a mnemonic, and the multiplication is
- Is There a Difference Between $d^2x$ and $ (dx)^2$?
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 $ (dx)^2=0$ but for two different reasons
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