What is an integral in a calculus equation which relates to physics?
914748
The funny looking S thing is an integral sign, the p stands for pressure and the dV stands for a little change in volume.\nIt sounds like the work performed by something expanding at constant pressure.  The work is the amount of energy used.
814825
Integrating the derivitive leaves you with the initial equation x^2 since an integral is the opposite to a derivitive much like addition is the opposite of subtraction.  If you add 2 then subtract 2 you have the same answer.  As for the area under the curve, this will indeed be your entire population.
1063457
Calculus is mathematics that deal often with the idea of infinity and non-linear (non-real) equations.  If we can develop mathematics that deal with these concepts, I think it proves we can understand the universe's infinite nature.
779428
I haven't got a clue what you are talking about, but the fundamental theorem of Calculus is that differentiation and integration are the reverse process of each other.\n\nThis link between differentiation and integration is what Newton and Leibniz discovered independently in the late 1600's.  There is a common mis-conception that Newton and Leibniz invented calculus, but calculus dates right back to the Greeks and Eudoxus and his method of exhaustion is the earliest form of integration.\n\nI think you need to re-word your question if you want some productive help.
889651
It's just arctan (x^2).\n\nBy the fundamental theorem of calculus, if F(t) is the antiderivative of f(t) = arctan(t^2), then the integral of f(t) from 0.5 to x will give F(x) - F(0.5). The derivative of this function with respect to x then gives you f(x).
897617
This is an equation with separated variables. Rewrite as \n\ndu/u^3 = (t^3-t)dt \n\nand integrate (find antideritive) of each side separately.
654738
Integral and differential calculus is a central branch of mathematics, developed from algebra and geometry. It is built on two major complementary ideas. The first is differential calculus, which studies the rate of change in one quantity relative to the rate of change in another quantity. This can be illustrated by the slope of a line. The second is integral calculus, which studies the accumulation of quantities, such as areas under a curve, linear distance traveled, or volume displaced. These two processes act inversely to each other, in a sense made specific by the fundamental theorem of calculus.\n\nExamples of typical differential calculus problems include:\n\nfinding the acceleration and velocity of a free-falling body at a particular moment. \nfinding the optimal number of units a company should produce to maximize their profit. \nExamples of integral calculus problems include:\n\nfinding the amount of water pumped by a pump with a set power input but varying conditions of pumping losses and pressure \nfinding the amount of parking lot plowed by a snowplow of given power with varying rates of snowfall. \nToday, calculus is used in every branch of the physical sciences, in computer science, in statistics, and in engineering; in economics, business, and medicine; and as a general method whenever the goal is an optimum solution to a problem that can be given in mathematical form. From a mathematical standpoint, it is used in conjunction with limits which, roughly speaking, allow the control or accurate description of an otherwise uncontrollable output.\n\nIntegral and differential calculus is a central branch of mathematics, developed from algebra and geometry. It is built on two major complementary ideas. The first is differential calculus, which studies the rate of change in one quantity relative to the rate of change in another quantity. This can be illustrated by the slope of a line. The second is integral calculus, which studies the accumulation of quantities, such as areas under a curve, linear distance traveled, or volume displaced. These two processes act inversely to each other, in a sense made specific by the fundamental theorem of calculus.\n\nExamples of typical differential calculus problems include:\n\nfinding the acceleration and velocity of a free-falling body at a particular moment. \nfinding the optimal number of units a company should produce to maximize their profit. \nExamples of integral calculus problems include:\n\nfinding the amount of water pumped by a pump with a set power input but varying conditions of pumping losses and pressure \nfinding the amount of parking lot plowed by a snowplow of given power with varying rates of snowfall. \nToday, calculus is used in every branch of the physical sciences, in computer science, in statistics, and in engineering; in economics, business, and medicine; and as a general method whenever the goal is an optimum solution to a problem that can be given in mathematical form. From a mathematical standpoint, it is used in conjunction with limits which, roughly speaking, allow the control or accurate description of an otherwise uncontrollable output.
183377
u may find it in calculus or in mechanics of wave test book
245944
The integral of a function over a definite interval.
9512
Imagine that you've integrated a function up to some value x.  Now, if you move to x+dx you get a sliver of area equal to f(x) times dx.  So the rate of change of the integral (the derivative of the integral) is just the value of the function.\n\nIn other words, how fast you're adding to the integral is the height of the function.
432536
Oops………..!\n\ndac2chari\n\n\n u = 1/(ln t) Then du = t dt ………………..?  How that come …!\n\nIf u = 1/(ln t) then  u = [ ln t ] ^-1 \n\nAnd  du = - [ln t ] ^-2 [ 1/t ] dt = dt / [-t (ln t ) ^2] … please be careful.\n------------------------------------------------------------------------------------\n\nOK… this integral can’t carry out using analytical method; however, the flowing one can be solve\n\n∫ dt / [t ln(t)] \n\nu = ln (t)\ndu =  dt / t  \n\nGives\n\n∫ dt / [t ln(t)]  = ∫ du/ u  ln(u)\n\nSubstitute for u\n\n∫ dt / [t ln(t)]  = ln [ ln (t) ]
859250
integral = x*tan(x)+ln(sec(x))  (use integration by parts with du = sec^2(x) and v = x).\n\ng'(x) = f(x), so a, c, e and g are true (b is true if f is continuous)\n\nSteve
728058
The integral is a special case.  It is:\n\nsqrt(pi/2)*erf(x/sqrt(2))\n\nBelow is a website to do integrals and the definition of the error function ('erf')
1143501
you can go to this site, you enter in the problem and it solves it for you....http://integrals.wolfram.com/index.jsp
1171650
In mathematics, a line integral (in rare cases called a path integral) is an integral where the function to be integrated is evaluated along a curve. Various different line integrals are in use. In the case of a closed curve it is also called a contour integral.
189548
Integrable Function.The idea of integration is twofold.\n\nWe may seek the function which has a given function as its differential coefficient, or we may generalize the question of finding the area of a curve. The first inquiry leads directly to the indefinite integral, the second directly to the definite integral. Following the second method we define the definite integral of the function f(s) through the interval between a and b to be the limit of the sum ~f(Xr) (x~ - X~_i)\n\nwhen the interval is divided into ultimately indefinitely small partial intervals by points 5i, XI, . . . X,,_i. Here x, denotes any point in the rth partial interval, Sf is put for a, and x~for b. It can be shown that the limit in question is finite and independent of the mode of division into partial intervals, and of the choice of the points such as x~, provided (I) the function is defined for all points of the interval, and does not tend to become infinite at any of them; (2) for any one mode of division of the interval into ultimatey indefinitely small partial intervals, the sum of the products of the oscillation of the function in each partial interval and the difference of the end-values of that partial interval has limit zero when n is increased indefinitely. &#92;Vhen these conditions are satisfied the function is said to be integrable in the interval. The numbers a and b which limit the interval are usually called the lower and upper limits. We shall call them the nearer and further end-values. The above definition of integration was introduced by Riemann in his memoir on trigonometric series (1854). A still more general definition has been given by Lebesgue. As the more general definition cannot be made intelligible without the introduction of some rather recondite notions belonging to the theory of aggregates, we shall, in what follows, adhere to Riemanns definition.\n\nWe have the following theorems:\n\nr. Any continuous function is integrable.\n\n2. Any function with restricted oscillation is integrable.\n\n3. A discontinuous function is integrable if it does not tend to become infinite, and if the points at which the oscillation of the (unction e~fceeds a given number e, however small, can be enclosed in partial intervals the sum of whose breadths can be diminished indefinitely.\n\nThese partial intervals must bea set chosen out of some complete set obtained by the process used in the definition of integration.\n\n4. The sum or product of two integrable functions is integrable.\n\nAs regards integrable functions we have the following theorems:\n\n1. If S and I are the superior and inferior limits (or greatest and least values) of f(x) in the interval between a and b, f f(x)dx is intermediate between S(ba) and I(ba).\n\n2. The integral is a continuous function of each of the end-values.\n\n3. If the further end-value b is variable, and if f f(x)dx=F(x), then if f(s) is continuous at b, F(s) is differentiable at b, and F(h) =f(b).\n\n4. In case f(s) is continuotis throughout the interval F(s) is continuous and differentiable throughout the interval, and F(x) =f(x) throughout the interval.\n\n5. In case f(s) is continuous throughout the interval between a and b, ff(x)4x =f(b) f(a).\n\n6. In casef(x) is discontinuous at one or more points of the interval between a and b, in which it is integrable, f f(x)dx is a function of x, of which the four derivates at any point of the interval are equal to the limits of indefiniteness off(s) at the point.\n\n7. It may be that there exist functions which are differentiable throughout an interval in which their differential coefficients are not integrable; if, however, F(x) is a function whose differential coefficient, F(-x), is integrable in an interval, then F(s) = fF(x)dx+const.,\n\nwhere a is a fixed point, and x a variable point, of the interval. Similarly, if any one of the four derivates of a function is integrable in an interval, all are integrable, and the integral of either differs from the orig
48881
Anytime you have a problem that is continuous, as opposed to discrete, you will need to use either integration or differentiation to characterize the solution.  That means to say that every problem that involves time in one way or another will necessitate the use of calculus to find an answer at some instant in time.  If the problem is such that you can approximate the answer, then you can discretize the parameters as small slices of time and come up with an approximate answer - without using calculus.