In calculus, an antiderivative, inverse derivative, primitive function, primitive integral or indefinite integral of a function f is a differentiable function F whose derivative is equal to the original function f. This can be stated symbolically as F' = f. The process of solving for antiderivatives is called antidifferentiation (or indefinite integration), and its opposite operation is called differentiation, which is the process of finding a derivative. Antiderivatives are often denoted by capital Roman letters such as F and G.Antiderivatives are related to definite integrals through the fundamental theorem of calculus: the definite integral of a function over an interval is equal to the difference between the values of an antiderivative evaluated at the endpoints of the interval.
In physics, antiderivatives arise in the context of rectilinear motion (e.g., in explaining the relationship between position, velocity and acceleration). The discrete equivalent of the notion of antiderivative is antidifference.
I am just curious I was thinking about this and if anyone could explain I would appreciate it. I am curious to know how to find the indefinite integral of xsinx with respect to x.
Thanks, David
Hi there,
Can someone explain to me what the following are and how each one is used as a tool for the next one:
1)Indefinite integral
2)Riemann Sum
3)Definite Integral
4)Fundamental Theorem of Calculus(The part which says that the derivative of the integral of f(t)dt from a to x is...
I've been trying to integrate the following function but have gotten somewhat stuck doing it. The answer i managed to produce gave some bogan answers.
the integral in question is
\int e^\frac{-(x-\mu)^2}{(2\sigma)^2}
where \mu and \sigma are constants.
its part of the normal...