Jun 27, 2019 · 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.

信号处理中，方差代表交流功率，即去除直流分量的功率。在概率论和统计学中，方差是 随机变量平均值的平方偏差 (the squared deviation from the mean of a random variable)。 一起温习下基础知识～ 1 …

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. …

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 ...

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 …

How to integrate $\int \frac {1} {\sin^4x + \cos^4 x} \,dx$? Ask Question Asked 11 years, 6 months ago Modified 3 years, 2 months ago

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 …

I just finished taking my first year of calculus in college and I passed with an A. I don't think, however, that I ever really understood the entire $\\frac{dy}{dx}$ notation (so I just focused on ...

For a definite integral with a variable upper limit of integration $\int_a^xf (t)\,dt$, you have $ {d\over dx} \int_a^xf (t)\,dt=f (x)$. For an integral of the form $$\tag {1}\int_a^ {g (x)} f (t)\,dt,$$ you would find the …

All proofs I have seen boil down to something similar. The above fact is useful in that it shows that right- and left-hand derivatives exist at each point, and hence it is locally Lipschitz. This is true in $\mathbb …