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: If the integral I can be shown to be zero, or if the real-valued integral that is sought is improper, then if we demonstrate that the integral I as described above tends to 0, the integral along R will tend to the integral around the contour R + I.
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If and integral
If one integrates this picture, which corresponds to applying the fundamental theorem of calculus, one obtains Cavalieri's quadrature formula, the integral – see proof of Cavalieri's quadrature formula for details.
If is any unit vector, the projection of the curl of F onto is defined to be the limiting value of a closed line integral in a plane orthogonal to as the path used in the integral becomes infinitesimally close to the point, divided by the area enclosed.
If φ is C < sup > k </ sup >, then the inhomogeneous equation is explicitly solvable in any bounded domain D, provided φ is continuous on the closure of D. Indeed, by the Cauchy integral formula,
If m and n are natural numbers and f ( x ) is a smooth ( meaning: sufficiently often differentiable ) function defined for all real numbers x in the interval, then the integral
If R is an integral domain then any two gcd's of a and b must be associate elements, since by definition either one must divide the other ; indeed if a gcd exists, any one of its associates is a gcd as well.
If and then the limit is where is the complete elliptic integral of the first kind
If R is an integral domain and f and g are polynomials in R, it is said that f divides g or f is a divisor of g if there exists a polynomial q in R such that f q = g. One can show that every zero gives rise to a linear divisor, or more formally, if f is a polynomial in R and r is an element of R such that f ( r ) = 0, then the polynomial ( X − r ) divides f. The converse is also true.
If the random variable is real-valued ( or more generally, if a total order is defined for its possible values ), the cumulative distribution function gives the probability that the random variable is no larger than a given value ; in the real-valued case it is the integral of the density.
If they are participant in the integral physical expression of a living human being who has absorbed and metabolized them, or if they are now the physical remains of a once-living human being, the substance of what they actually are is human, hence, a human body.
If the liquid is incompressible the molar volume is constant and the integral becomes.
If the baseline value is large or if it is not subtracted out of the image, then the computed D4σ value will be larger than the actual value because the baseline value near the edges of the sensor are weighted in the D4σ integral by x < sup > 2 </ sup >.
If g is large and b is small so that the angle is not negligible one can write the integral for the on-axis case ( P < sub > 1 </ sub > is at the center of the shadow ) as ( see ):
Lebesgue presents six conditions which it is desirable that the integral should satisfy, the last of which is " If the sequence f < sub > n </ sub >( x ) increases to the limit f ( x ), the integral of f < sub > n </ sub >( x ) tends to the integral of f ( x ).
If f represents a very small but intense source of heat, then the preceding integral can be approximated by the delta distribution, multiplied by the strength of the source.
If r < 1, the derivatives of φ may be computed by differentiating under the integral sign, and one can verify that φ is analytic, even if u is continuous but not necessarily differentiable.
If R = K is a field, then K (( X )) is in fact a field, which may alternatively be obtained as the field of fractions of the integral domain K < nowiki ></ nowiki > X < nowiki ></ nowiki >.
If R possesses no zero divisors, it is called an integral domain since it closely resembles the integers in some ways.
* If R is an integral domain, the units of the Laurent polynomial ring RX < sup >− 1 </ sup > have the form uX < sup > k </ sup >, where u is a unit of R and k is an integer.
If we take such a tiling and enlarge it so that the formerly smallest tile now has the size of the square S we started out from, then we see that we obtain from this a tiling of the plane with integral squares, each having a different size.
If the index is over, then the sum is not defined and is replaced by an integral instead.
If the boundary is piecewise smooth, then we interpret the integral as the sum of the corresponding integrals along the smooth portions of the boundary, plus the sum of the angles by which the smooth portions turn at the corners of the boundary.
If the situation is as above but the extension L of K is algebraic of infinite degree, then it is still possible for the integral closure S of R in L to be a Dedekind domain, but it is not guaranteed.
If and I
If I could make myself feel the same way
If I don't come back in the house, Breed's going to '' --
If I hadn't got Nate stopped when I did, my duds'd all be shot plumb to hell!!
I showed her the shower and tub, and she said, smiling, `` If you really don't mind, I think I'll get clean in the shower, then soak for a few minutes in your tub.
If it were not for an old professor who made me read the classics I would have been stymied on what to do, and now I understand why they are classics ; ;
If I even hint at it do you think it will matter that you are his nephew -- and not even a blood nephew ''??
If you tell him I made a pass at you he might think you misunderstood something I said or did, so instead of just telling him I made a pass, say I tried to date you and that you agreed so you could prove to him what a louse I really am.
If it were not that I knew who it was I could have mistaken it for my Aunt so well did her clothes fit him.
Fruit compote: `` If you think I would understand it '' ; ;
`` If you will pardon, I think it would be better if not.
`` If I don't come out within half an hour ride back to town and bring out a posse ''.
If the old fool argues about the price, tell him I shall order my husband not to treat him as a patient any longer.
If I now risk some comparisons with Sons And Lovers let it be clear that I am not comparing the two works or judging their merits ; ;
If Mrs. Wright doesn't accept the terms in the morning, I'll go either to Tokyo or to Holland, to do what I can.
If I am to speak the whole truth about my knowledge of love, I will have to stop trying to emulate the transcendant nightingale.
If and can
If any of us miss, they can pick up the pieces.
`` If you can conveniently let me have twenty dollars '', he wrote one friend in 1791 when he was Secretary of the Treasury.
If we cannot stop warfare in our own economic system, how can we expect to abolish it internationally??
If our sincerity is granted, and it is granted, the discrepancy can only be explained by the fact that we have come to believe hearsay and legend about ourselves in preference to an understanding gained by earnest self-examination.
If within one year you can make a success out of the American, you can practically name your own salary thereafter.
If it is not one of his best books, it can only be considered unsatisfactory when compared with his own Garibaldi.
If there be a disinterested patriot in America, 'tis General Washington, and his bravery, none can question ''.
`` If you can firmly make the good knight sure to pleasure our Corporation '', Sturley wrote, `` besides that ordinary allowance for your diet you shall have 20 for recompence ''.
If man is actually the product of his environment and if science can discover the laws of human nature and the ways in which environment determines what people do, then someone -- a someone probably standing outside traditional systems of values -- can turn around and develop completely efficient means for controlling people.
If the manner of his passing moves the nations to act in the spirit of his dedication the sore issues that plague the world can yet be resolved with reason and justice.
If they do as well as they did in 1960 there can be no complaint.
If he can bounce back with one of those 25 home runs years, the club will have to be better off offensively.
If it will simply delay the debates until the qualifications are closed next spring, and then carry all the candidates on a tour of debates, it can provide a service to the state.
`` If the day should ever come that foreign invaders swarm ashore along the Gulf Coast '', the account reads, `` they can count on heavy opposition from a group of commando-trained telephone employees -- all girls.
If we cluster together, the redcoats can make an advantage out of it, but there's not a blessed thing they can do with two or three of us except chase us, and we can outrun them ''.
If there is anything which we can do in the executive branch of the Government to speed up the processes by which we come to decisions on matters on which we must act promptly, that in itself would be a major contribution to the conduct of our affairs.
If the target can change its position significantly during the 30 minutes the missile is in the air on its way, the probability of the missile destroying the target is drastically reduced.
If your state has no provisions for the numbering of pleasure boats, you must apply for a number from the U.S. Coast Guard for any kind of boat with mechanical propulsion rated at more than 10 horsepower before it can be used on Federal waterways.
If there are any major restrictions, they usually can be obtained in printed form.
Note: If 1/2-inch panel board is used inside and out, or 5/8-inch one side and 3/8-inch the other, and 1/8-inch glass is used, stock lumber in Af, Af, and Af can be used in making the glass panels.
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