What is Integrating: Definition and 971 Discussions

In mathematics, an integrating factor is a function that is chosen to facilitate the solving of a given equation involving differentials. It is commonly used to solve ordinary differential equations, but is also used within multivariable calculus when multiplying through by an integrating factor allows an inexact differential to be made into an exact differential (which can then be integrated to give a scalar field). This is especially useful in thermodynamics where temperature becomes the integrating factor that makes entropy an exact differential.

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  1. A

    Integrating through partial fractions

    here's the problem, i am supposed to take the integral from 1 to 2 of this: (dx)/[(X+3)^2 (x+1)^2] I decided that the easiest way to compute it is by integrating by partial fractions so what i did was set up the equation: A/(x+3) + B/[(x+3)^2] + C/(x+1) + D/[(X+1)^2] = 1 After this I...
  2. F

    Integrating nested root in denominator

    Hi Y'all, I was trying to integrate a function in two dimesions. after integrating it in one dimesion and substituting the limits I got two terms. I am unable to integrate the second term. That is because it had a sqare root in the denominator which contained another one within it. I took...
  3. D

    Learn How to Integrate x^x with Ease | Expert Tips and Tricks

    how do you integrate x^x dx? Thx
  4. A

    Help with integrating these simple functions

    how do i integrate sqrt(3-(x^2))/sqrt(3)? i put the sqrt(3) outside the integral and tried using the substitution method to integrate it but there is still an x in there? same thing with integrating sqrt(3-3*(x^2)) Thanks! This thing is due tomorrow.. :eek:
  5. A

    Integrating gravity(g)= -9.8m/s

    correct me if I am wrong... By integrating gravity(g)= -9.8m/s...you get the motion equations with constant acceleration I didnt know how to set the limits of the integral...LATEX IS TUFF d\vec{a}=(-g)dt 1 \int_{\vec{V}_0}^{\vec{V}}dv=\int_{t_0}^{t_1}{-g}dt 2 \Delta{\vec{v}}=(-g)t...
  6. A

    Integrating V = V(initial) + at

    sorry i didnt use latex..I tried...its annoying V=V(initial) + at...when you integrate both sides you get x=x(initial) + ..? I had a little trouble trying to integrate the (at) do you use the uv-integral(v DV) theorm...well i used that and it and it didnt give me the second equation for...
  7. A

    Cylindrical shells trouble integrating

    i'm told to use the method of cylindrical shells to find the volume gnerated by rotating the region bounded these curves about the y axis: y=e^(-x^2) y=0 x=0 x=1 Couple questions. What does the graph of y=e^(-x^2) look like? Also, i know the integral is =integral(a,b) 2(pi)x*e^(-x^2) how...
  8. W

    Simplifying and Integrating Cosine Functions

    \int 96cos^4(6x) * dx ok first i take out the 96 cause it's constant! 96 \int cos^4(6x) * dx 96 \int (cos^2(6x)^2) * dx ok now with that setup, i can know use the half-angel formula! 96 \int (\frac{1+cos(12x)}{2})^2 squared the problem... 24 \int (1+ 2cos(12x) +...
  9. O

    Integrating tan(x): Solving the Absolute Value Puzzle

    Today I was reading my favorite calculus textbook, that saw the integration formula for tan(x). It was : Integral of tan(x) = -ln|cosx| + C . I know that when we say integral of tanx we mean, what is the function whose derivative is tanx. So started to take the derivative of -ln |cosx|, in...
  10. H

    Having troubles integrating e^(2x)sin(x)

    Hi, I have to integrate this: \int e^{2x}sinx I've tried by parts, but e^{2x} never goes away and sinx just keeps going back and forth to cosx. Is there some kind of substitution I should use? The original question was the differential: (-e^xsinx+y)dx+dy = 0 and I'm trying to...
  11. Math Is Hard

    Solving a Linear Equation with e^(x^2) Integrating Factor

    I am trying to solve a linear equation and getting stuck. y' + 2xy = x^2 I am using e^{x^2} as my integrating factor and multiplying that to both sides. Afterwards, I am able to wrap up the LHS as [y e^{x^2}]' and I have [y e^{x^2}]' = x^2 e^{x^2} Now all I need to do is...
  12. S

    How Can We Integrate 1/(u*sqrt(1-u^2))?

    Int(cosec x)dx Let: u=cos x then: x=arcos u and: dx=-du/sqrt(1-u^2) Int(cosec x)dx = -Int{1/sqrt(1-u^2)}^2}du = -Int {du/(1-u^2)} = -(1/2)ln(1-u^2) + C =...
  13. Jeebus

    Integrating Trigonometric Functions: Need Help!

    I need help with these problems: (1) STan^-1(y)dy and (2) Ssin^-1(x)dx (S=integral) I can't seem to figure out the trigonometric formula for integration. A little help or hint would be nice. Thanks!
  14. Math Is Hard

    Integrating a logarithmic function

    I noticed than in the chapters I am studying now that while they give us a formula for taking the derivative of log base a of x, I can't find a correspoding formula for finding the integral of log base a of x. We have a table of integrals in the back of the book, but I only see integrals...
  15. A

    Integrating 1/x^3: -2/x^2 or -1/2x^2?

    Hi, ive got a really simple question, but I am just slightly confused, im trying to integrate 1/x^3 , now i take x^3 to the top and i get x^-3, and now when i intergrate that i get: x^-2/-2 (i think) now when i put it back into fractional form do i get: -2/x^2 or -1/2x^2 ?
  16. S

    Integrating sinx/x between (0,infinty)?

    integrating sinx/x between (0,infinty)? hey ppl! Can you help me by giving me a method or how you would go around to prove that this \mid\int\frac{sinx}{x}dx\mid exists. Thanx Saint_n
  17. B

    Integrating the Normal Distribution Curve

    Given P(x)= \frac{1}{\sigma \sqrt{2\pi}} e ^ \frac { -(x - \mu )^2}{2 \sigma ^2 } This is of course the normal distribution curve. When \mu = 0 and \sigma = 1 I can integrate this from minus infinity to positive infinity no problem using polar coordinates and a bit of multivariable...
  18. B

    Integrating (3-x)7^[(3-x)2]: A Step-by-Step Guide

    Need a kickstart with this one: f(t)=t^(3/2)log(of 2)Sqrt(t+1) Integral of (3-x)7^[(3-x)^2] dx 7^[(3-x)2] = e^[(3-x)2ln 7] u=(3-x)^2 du/dx = -2(3-x) (3-x)dx = -1/2 du not even sure what so far is right..
  19. ShawnD

    How can I integrate and find the moment of inertia for a circle?

    In school, I'm doing this thing called moment of inertia given by the formula I = \int y^2 dA If the object being solved for is a rectangle where the base of it is parallel to the x axis, dA is equal to xdy. From there, the integration is easy. If the object to solve the integration for is...
  20. S

    Integrating rational functions

    I've just finished reading the section on partial fraction integration from my text. The book describes how all rational functions can be integrated by performing a partial fraction decomposition and subsequently integrating the partial fractions using methods that are already known. I tried to...
  21. M

    How can I integrate 1/(1+e^x) by substituting u = e^{-x} + 1?

    Integrating 1/(1+e^x): I am currently substituting 1+e^x = u, S (u*e^x)^-1 du since du/dx = e^x S (u*(u-1))^-1 du (S represents the integral symbol) But i looked up the answer and got Ln (e^x(1+e^x)) +c i need to understand how this is done, thanks in advance everyone.
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