Integrating Definition and 940 Threads

  1. RadiationX

    Integrating e^x/(e^{2x} + 1): Long Division?

    i'm having trouble rewriting this integral:\int\frac{e^x}{e^{2x} + 1} so that it will be in the arctan formula: should i use long divison here? if it were not for the e^x in the numerator i'd be fine.
  2. N

    How to Motivate the Integrating Factor Strategy for \( \mu(y) \)?

    Q. Motivate the Integrating factor strategy for U ( "Mew" ) of y I know how to prove it for "Mew" of x but how to do for "mew" of y Maybe something like this. Mdx (x.y) + Ndy ( x, y ) = 0 Assume this is differentiable so let us multiply by "mew" of x on both sides to make it...
  3. M

    Integrating a 3x3 orientation matrix

    Hi there, (I hope this post is in the right forum) I'm trying to integrate a 3x3 orientation matrix using a vector representing rotational velocity (in 3d) This is the formula I'm using: newOrientation = orientation + (dt)(~w)(orientation) where w is the vector rotational velocity...
  4. A

    Help Integrating Tripple Integral for x+y+z=1

    the question is "evaluate \iiint z \,dv, of a solid tetrahedron bounded by the four planes x=0,y=0,z=0, and x+y+z=1" I can set up the problem correctly but i can't seem to integrate it right \int_{0}^1 \int_{0}^{1-x} \int_{0}^{1-x-y} z dzdydx (1/2) \int_{0}^1 \int_{0}^{1-x} (1-x-y)^2dydx...
  5. A

    Integrating Population Differential Equation: Need Help!

    I have this population differential equation dP/dt=k1(P)-k2(P) where k1 and k2 are proportionality constants. I need to integrate and analyze where k1>k2, k1=k2, and k1<k2. Trouble is, I don't think I'm integrating this right. I get P=e^(t+C)(k1-k2). I know this should be easy but I don't think...
  6. D

    Integrating $\frac{1}{\sqrt{2\beta x-\alpha x^2}}$

    Does anyone know how to intergrate \frac{1}{\sqrt{2\beta x-\alpha x^2}} I went to wolfram and type it in, but it gave me a weird number.
  7. B

    How Do You Integrate a Wave Function to Find Electron Probability?

    Hey. I am pretty confident i have solve this problem. I just solve the integral of the given wave function, with the given limits... However, I am having a difficult time integrating it. The sqrt(2/L) can be brought outside of the integral, but what can i with the sin function? The wave...
  8. J

    How do you determine which denominators to multiply in integrating fractions?

    We just started this and I mostly understand it except when it comes to using A, B, C, etc substitution. What I mean is this, here is an exampe. (6x^2+x+1)/(x^2+1)(x-1) = (Ax+B)/(x^2+1) + (C)/(x-1) You then multiply by denominators so you end up with (Ax+B)*(x-1) + (C)*(x^2+1). You...
  9. C

    Integrating an Improper Divergent Integral & Ellipsoid Volume

    I need help with two questions. Find a divergent improper integral whose value is neither infinity nor -infinity. 2. Find the volume of an ellipsoid (a^2*x^2) + (b^2*8y^2) + (c^2*z^2) = a^2*b^2*c^2 using integration.
  10. M

    Integrating Polar Equations: Online Resources

    Can anyone point me to some online resources on how to integrate polar equations? Thanks.
  11. A

    Can you integrate sin(sqrt(x)) using a trigonometric substitution?

    I need to know how to integrate this function: sin(sqrt(x)) I did this: u = sqrt(x) du/dx = 1/(2sqrt(x)) S(sin(sqrt(x))dx) = S(sin(u)*dx*du/dx/(2sqrt(x)) = S(Sin(u)/u du) But then I got stuck: integration by parts won't work, trig substitution is out... The one thing I did come up...
  12. T

    Integrating and differentiating the number e.

    In calculus, my work has recently involved integrating and differentiating the numer e, of which I am very unsure of how to do. I set up some examples for myself to try to figure out, could anyone tell me if they are correct? Please correct me if I am wrong, or tell me where I have made a...
  13. C

    Why the modulus signs when integrating f'(x)/f(x)?

    I am able to proove to myself, through generalised substitution, that the integral of f'(x)/f(x) is lnf(x)+c, but where do the modulus signs come from? ie - The accepted integral is ln|f(x)|+c, not lnf(x)+c Thanks in advance. :smile:
  14. N

    Need Help - Exact Integrating Factor?

    Here's the problem: y\left( 2x-y-1 \right) dx + x\left( 2y-x-1 \right) dy = 0 So rewrite it as: \left( 2xy-y^2-y \right) dx + \left( 2xy-x^2-x \right) dy = 0 Now it's in the form,…P(x,y) dx + Q(x,y) dy = 0 \frac{\partial P(x,y)}{\partial y} = 2x-2y-1 \frac {\partial...
  15. D

    Integrating tan^2(u)(sec(u))du: Is There a Clean Way?

    whats the integral of tan^2(u)(sec(u))du? i was trying to integrate (x^2)/sqrt(x^2+1)dx, and came into that. it turns out pretty messy though, is there a clean way to do it?
  16. U

    Integrating Force: Understanding \oint and \int

    does the integration of Force equal negative potential energy? \int{F}={-U} Also, what is the difference between \oint and \int?
  17. D

    Integrating csc(x): Easier Than You Think

    haven't found a way of doing it so far. I have a feeling that it's extremely easy, and I'm missing how to do it somehow :/
  18. M

    How Do You Integrate the Function 1/x?

    Yeah, this questions may be a little elementary for some, but I don't seem to have any sources which would be able to tell me how do i integrate a function 1/x. Any help would be great. : )
  19. N

    Integrating the ALLEE Effect: ds/dt = -a s ln(bs)

    how can i integrate the equation presenting the ALLEE EFFect ds/dt = - a s ln(bs) where a and b are constants
  20. 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...
  21. 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...
  22. D

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

    how do you integrate x^x dx? Thx
  23. 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:
  24. 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...
  25. 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...
  26. 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...
  27. 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) +...
  28. 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...
  29. 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...
  30. 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...
  31. 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 =...
  32. 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!
  33. 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...
  34. 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 ?
  35. 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
  36. 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...
  37. B

    How Do You Integrate Functions Involving Exponents and Substitutions?

    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..
  38. 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...
  39. 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...
  40. 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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