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A function f(x) is said to be square integrable if int_(-infty)^infty|f(x)|^2dx is finite.

A triple integral is a three-fold multiple integral of the form intintintf(x,y,z)dxdydz. Triple integrals arise in evaluating quantities such as the mass, volume, moment, ...

A multiple integral is a set of integrals taken over n>1 variables, e.g., int...int_()_(n)f(x_1,...,x_n)dx_1...dx_n. An nth-order integral corresponds, in general, to an ...

The computation of a derivative.

The Leibniz integral rule gives a formula for differentiation of a definite integral whose limits are functions of the differential variable, (1) It is sometimes known as ...

If g is continuous and mu,nu>0, then int_0^t(t-xi)^(mu-1)dxiint_0^xi(xi-x)^(nu-1)g(xi,x)dx =int_0^tdxint_x^t(t-xi)^(mu-1)(xi-x)^(nu-1)g(xi,x)dxi.

Not continuous. A point at which a function is discontinuous is called a discontinuity, or sometimes a jump.

Let g(x)=(1-x^2)(1-k^2x^2). Then int_0^a(dx)/(sqrt(g(x)))+int_0^b(dx)/(sqrt(g(x)))=int_0^c(dx)/(sqrt(g(x))), where c=(bsqrt(g(a))+asqrt(g(b)))/(sqrt(1-k^2a^2b^2)).

Let f(z) be an analytic function in |z-a|<R. Then f(z)=1/(2pi)int_0^(2pi)f(z+re^(itheta))dtheta for 0<r<R.

U_n(f)=int_a^bf(x)K_n(x)dx, where {K_n(x)} is a sequence of continuous functions.