Antiderivatives are important because they can be used to compute definite integrals, using the fundamental theorem of calculus: if F is an antiderivative of the integrable function f, then:

The intimations of a related spirit and ordering of human values are stronger than any sense of disparity.

Rousseau's primitivism, the anti-Newtonian mythology of Blake, Coleridge's organic metaphysics, Victor Hugo's image of the poets as the Magi, and Shelley's `` unacknowledged legislators '' are related elements in the rear-guard action fought by the romantics against the new scientific rationalism.

In addition, there are many areas of the human situation besides the impact of science and technology which are examined, for science-fiction dystopias often extrapolate political, social, economic tendencies only indirectly related to science and technology.

To hang 50 Governors might be preferable except that they are not directly related to the highways ; ;

These roads are largely of less than highway standards, and usually carry traffic which is related to use of the National Forests.

A signal cannot be cleared until all the related turnouts are properly thrown and locked.

Such an instrument is expected to be especially useful if it could be used to measure the elasticity of heavy pastes such as printing inks, paints, adhesives, molten plastics, and bread dough, for the elasticity is related to those various properties termed `` length '', `` shortness '', `` spinnability '', etc., which are usually judged by subjective methods at present.

Although there is no question but that the process of washing fabrics involves a number of phenomena which are related together in an extremely complicated way and that these phenomena and their interrelations are not well understood at the present, this section attempts to present briefly an up-to-date picture of the physical chemistry of washing either fabrics or hard surfaces.

Closely related to the andrenas are the nomias or alkali bees.

Perhaps a clue to these and related problems lies in the fact that changes in the intensity of hypothalamic discharges which are associated with changes in its balance lead also to qualitative alterations in reactivity.

Furthermore, conditioned reactions are fundamentally altered when the hypothalamic sympathetic reactivity is augmented beyond a critical level, and several types of behavioral changes probably related to the degree of central autonomic `` tuning '' are observed.

Isolated enterprises have been launched, but they are not yet related to each other in a meaningful pattern.

There are several closely related inner functions.

Closely related to this function is the fact that the religious system provides a body of ultimate ends for the society, which are compatible with the supreme eternal ends.

Nevertheless I consider it reasonable, because of my commitment as an artist, to assume that the rights and responsibilities of creative individuals are related to humanity as a whole rather than to specific geo-political interests.

In another study chromium-substituted aluminum oxyhydroxides and related species, prepared homogeneously by high-temperature hydrolysis, are being characterized and investigated spectrally in the ultraviolet region with a view to identification and semiquantitative estimation of the phases formed under varying preparative conditions.

Therefore employment and education in all the schools in a metropolitan area are related in different ways from those which are characteristic of the comprehensive high school described in my first report.

These structures are intimately related to social attachment and bonding in other species.

A 2005 molecular phylogeny based on rDNA analysis suggests that salamanders and caecilians are more closely related to each other than they are to frogs.

The order Caudata ( from the Latin cauda meaning " tail ") consists of the salamanders, elongated, low-slung animals that mostly resemble lizards in form, though this is a symplesiomorphic trait and the two groups are no more closely related than salamanders are to mammals.

In a certain perfectly definite way, the method and the theme of his stories are one and the same.

In urethane foams, for example, there has been a definite trend toward the polyether-type materials ( which are now available in two-component rigid foam systems ) and the emphasis is definitely on one-shot molding.

Some alphabets today, such as the Hanuno ' o script, are learned one letter at a time, in no particular order, and are not used for collation where a definite order is required.

Since all energies are measured relative to the vacuum, H is positive definite.

There are no definite earlier bows ; previous pointed shafts are known, but may have been launched by spear-throwers rather than bows.

Though the model showed no significant changes to the climate in areas other than the Tropics, this may not be the case since the model has possible errors and the results are never absolutely definite.

And for the writing of detective stories there are very definite laws — unwritten, perhaps, but nonetheless binding ; and every respectable and self-respecting concocter of literary mysteries lives up to them.

The terms divinity and divine — uncapitalized, and lacking the definite article — are sometimes used as to denote ' god ( s ) or certain other beings and entities which fall short of godhood but lie outside the human realm.

These terms are normally used with the definite article in Goidelic languages, causing lenition in all cases: An Cháisc, A ' Chàisg and Y Chaisht.

One supposes that the quantum spin-singlet states emitted by the source are actually approximate descriptions for " true " physical states possessing definite values for the z-spin and x-spin.

When the intermediate states at intermediate times are energy eigenstates ( collections of particles with a definite momentum ) the series is called old-fashioned perturbation theory.

When it comes to the matter of practical farm managing which will secure definite, practical, financial results, you are wanting again in ability.

" In the social production of their existence, men inevitably enter into definite relations, which are independent of their will, namely relations of production appropriate to a given stage in the development of their material forces of production.

There are definite examples of humor restricted by copyright law on the internet ; examples include the Dilbert cartoons of Scott Adams or the newspaper columns of Dave Barry.

The integrals discussed in this article are termed definite integrals.

The exact charges are not known, as the matter did not get as far as a definite examination.

That the several states composing the United States of America are not united on the principle of unlimited submission to their general government ; but that, by compact, under the style and title of a Constitution for the United States, and of amendments thereto, they constituted a general government for special purposes, delegated to that government certain definite powers, reserving, each state to itself, the residuary mass of right to their own self-government ; and that whensoever the general government assumes undelegated powers, its acts are unauthoritative, void, and of no force ; that to this compact each state acceded as a state, and is an integral party, its co-States forming, as to itself, the other party ; that this government, created by this compact, was not made the exclusive or final judge of the extent of the powers delegated to itself, since that would have made its discretion, and not the Constitution, the measure of its powers ; but that, as in all other cases of compact among powers having no common judge, each party has an equal right to judge for itself, as well of infractions as of the mode and measure of redress.

There are several species from the Eocene, such as Petermanniopsis anglesaensis or Smilax, but their identification is not definite.

It also became clear that such clauses could be restricted to definite clauses or Horn clauses, where < tt > H </ tt >, < tt > B < sub > 1 </ sub ></ tt >, …, < tt > B < sub > n </ sub ></ tt > are all atomic predicate logic formulae, and that SL-resolution could be restricted ( and generalised ) to LUSH or SLD-resolution.

The integrals ( in units ) are listed in table 14-1, below.

( There are a large number of other known integrals and identities that are not reproduced here, but which can be found in the references.

Incomplete elliptic integrals are functions of two arguments ; complete elliptic integrals are functions of a single argument.

thus, the Jacobian elliptic functions are inverses to the elliptic integrals.

There are still other conventions for the notation of elliptic integrals employed in the literature.

On the ellipsoid of revolution, geodesics may be written in terms of elliptic integrals, which are usually evaluated in terms of a series expansion ; for example, see Vincenty's formulae.

In mathematical analysis, integrals dependent on a parameter are often considered.

Techniques from the theory of analytic functions of a complex variable are often used in real analysis – such as evaluation of real integrals by residue calculus.

No function has this property, but it can be thought of as a limit of functions whose integrals over space are unity, and whose support ( the region where the function is non-zero ) shrinks to a point ( see weak solution ).

0 are equal everywhere except at x = 0 yet have integrals that are different.

According to Lebesgue integration theory, if ƒ and g are functions such that ƒ = g almost everywhere, then ƒ is integrable if and only if g is integrable and the integrals of ƒ and g are identical.

These two integrals are the definitions of and, so:

Derivatives and definite integrals are evaluated exactly when possible, and approximately otherwise.

They are widely used in mathematics, for example to evaluate multidimensional definite integrals with complicated boundary conditions.

where d < sup > 3 </ sup > k = dk < sub > x </ sub > dk < sub > y </ sub > dk < sub > z </ sub > is the differential volume element in k-space, and the integrals are taken over all k-space.