|
- calculus - Is there really no way to integrate $e^{-x^2 . . .
$\begingroup$ @user599310, I am going to attempt some pseudo math to show it: $$ I^2 = \int e^-x^2 dx \times \int e^-x^2 dx = Area \times Area = Area^2$$ We can replace one x, with a dummy variable, move the dummy copy into the first integral to get a double integral
- integration - Differentiating Definite Integral - Mathematics Stack . . .
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 derivative using the chain rule As stated above, the basic differentiation rule for integrals is:
- Calculus proof for the area of a circle
$\begingroup$ @andreas vitikan Note that your teacher's approach is what Jennifer Dylan describes above, and while the calculation of that integral is more difficult, the idea behind it is quite straightforward On the other hand, the integral you have is quite easy to calculate but the background is not as intuitive, IMHO
- How to calculate the integral in normal distribution?
It goes without saying that if you're trying to find a CDF, you need to add limits and evaluate the definite integral In the second equation you'll notice that I used "a" as the (upper) limit variable And the question is talking about the CDF, so the lower limit is negative infinity $\endgroup$ –
- What is the integral of - Mathematics Stack Exchange
Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
- The volume of sphere using integrals - Mathematics Stack Exchange
Integral for volume under a sphere bounded by a square 0 Calculating Volume of Spherical Cap using
- calculus - integral of $\text {abs} (\sin (x))$ explanation . . .
Discrepancy in definite integral $\int_{0}^{2\pi}\frac{1}{10+3\cos x}dx$ using Desmos 1 Finding the limit value for a given percentage of total area of half sine wave
- integration - reference for multidimensional gaussian integral . . .
The presentation here is typical of those used to model and motivate the infinite dimensional Gaussian integrals encountered in quantum field theory
|
|
|