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4 dni temu · The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at each point in time) with the concept of integrating a function (calculating the area under its graph, or the cumulative effect of small contributions). Roughly speaking, the two operations can be ...
5 dni temu · A function which is the product of two different kinds of functions, like \(xe^x,\) requires a new technique in order to be integrated, which is integration by parts. The rule is as follows: \[\int u \, dv=uv-\int v \, du\] This might look confusing at first, but it's actually very simple.
4 dni temu · In mathematics, particularly multivariable calculus, a surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analogue of the line integral.
6 dni temu · Here's another way to find the area of the loop below the x-axis, using the Green's-theorem area formula and NDSolve to perform the line integral. The value for area300 is the 300-digit result from my other answer, used to check the accuracy of the NDSolve result.
4 dni temu · In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve. [1] The terms path integral, curve integral, and curvilinear integral are also used; contour integral is used as well, although that is typically reserved for line integrals in the complex plane.
5 dni temu · I used a contour into the upper half of the complex plane to make the integral $R_m$ converge better, and calculated it with the double-exponential option of NIntegrate[]. Here is the (not well-written)) code, designed to show how the number of correct digits increases with $N$:
5 dni temu · Arbitrary Constant of Integration -- from Wolfram MathWorld. Calculus and Analysis. Calculus. Integrals. Indefinite Integrals.
