The Fundamental Theorem of Calculus is a cornerstone of calculus, linking the concepts of differentiation and integration. This video provides a thorough and accessible explanation of this important ...
in this section we're going to cover what we call the fundamental theorem of calculus and as you can guess with a title like that it's pretty darn important basically what we've done in the last ...
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.
What would you set the limits if you need to calculate the area of an infinitesimal ring in cartesian coordinates i.e. $\int dx \int dy $.. where you only want to integrate on the infinitesimal ring.. I know in polar that will be 2Ď€rdr but how will you get it in caartesian using double integral
Surface Integral over a sphere Ask Question Asked 11 years, 8 months ago Modified 11 years, 8 months ago
I was reading on Wikipedia in this article about the n-dimensional and functional generalization of the Gaussian integral. In particular, I would like to understand how the following equations are
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 such as $\frac {x^3} {3} +C$. However, the indefinite integral from $ (-\infty,\infty)$ does exist and it is $\sqrt {\pi}$ so explicitly: $$\int^ {\infty}_ {-\infty} e^ {-x^2} = \sqrt {\pi}$$ Note ...