Integrate Definition and 642 Threads

  1. J

    I have to integrate int_0^1 sqrt(t^2-1)dt

    I was wondering how to solve this integral: \int_{0}^{1}\sqrt{t^2-1}\,dt When I punch it into mathematica, it gives: 1/2 t\sqrt{-1+t^2}-1/2\log{(t+\sqrt{-1+t^2})} I was wondering what steps are done to get this result I suppose I forgot to enter it in as a definate integral, but still...
  2. H

    How do high level academics acquire and integrate information?

    I recently have begun taking university classes again, and I have been reminded of the impressive breadth and depth of knowledge wielded by professors. I'm interested in getting some insight into how they do it, both because it's an interesting question in its own right and because I would like...
  3. N

    How to evaluate the integral of dv/(1+(A/(mg))alpha*v) from [vo,v] = -gt?

    Someone please tell me how to integrate dx/(1+e^x). Thanks
  4. M

    Forgot how to integrate yes t*cos(Pi*t)

    forgot how to integrate! yes! t*cos(Pi*t) Hello everyone I'm integrating a position vector and I'm stuck on integrating the j unit. t*cos(Pi*t); the answer i got with maple is: 1/Pi^2*(cos(Pi*t)+Pi*t*sin(Pi*t)) but i have no idea how maple busted that out. if i let u = cos(Pi*t); du =...
  5. L

    Ideas as to how I should start to integrate this one?

    \int (C^2x^2-x^4)^{0.5} dx C is a constant any ideas as to how I shoud start to integrate this one?
  6. I

    How can I integrate a sinusoidal current in an L-C circuit undergoing resonance?

    An L-C circuit will undergo resonance, with the current varying sinusoidally, where: I(t) = I*cos(omega*t) I keep getting stuck with an answer of I*t*sin(omega*t) Can't find anything on the standard table of integrals that would indicate this is incorrect :confused:
  7. J

    How can I solve this integral using integration by parts?

    Hi , I am having trouble integrating this problem. Integrate x^2 sin(x^2) dx Here is what i did. I used the substitution method. u = x^2 sqrt u = x du = 2x dx du/2x = dx du/2 sqrt u = dx since sqrt u = x substituting this in the equation u sin(u)...
  8. M

    How Do I Integrate sqrt(4x) + sqrt(4x) on the Interval 0 to 1?

    Ok, I've been doing work for about 4 hours straight and I think my brain is fried. I know this is easy, it is just not working in my head. Anyway, the problem is this: Integrate the sqrt(4x) + sqrt(4x) on the interval 0 to 1 I get, (8^3/2)/3 + (8^3/2)/3 but apparently this is not right...
  9. M

    What is the correct way to integrate sqrt(4x) + sqrt(4x) on the interval 0 to 1?

    Ok, I've been doing work for about 4 hours straight and I think my brain is fried. I know this is easy, it is just not working in my head. Anyway, the problem is this: Integrate the sqrt(4x) + sqrt(4x) on the interval 0 to 1 I get, (8^3/2)/3 + (8^3/2)/3 but apparently this is not...
  10. L

    How do I find the integral of ln x?

    this is an honest question. i have attempted this but i didnt know how to do this. tomorrow is my exam and i realized that there was no where of finding the integration of y=lnx. everytime i ask tis question, people will tell be 1/x but that is the derivative, i am after the integral so is...
  11. L

    How Can I Integrate sqrt(2+2sin(x))?

    I'm having trouble with this. Can anyone help me integrate sqrt(2+2sin(x)) ?? Thanks
  12. G

    How to integrate int (x^2 + 4)^(-1/2) dx Is it a substitution?

    I need help antidiffing this equation: (x^2+4)^(-1/2) i have tried subbing u=x^2+4 i have tried subbing u= (x^2+4)^(-1/2). i have tried making x the subject. even tried to use partial fraction, with no avail, because i could not figure out how to use partially factorize it. If anyone could...
  13. L

    Why is it difficult to integrate x^x

    I tried doing this but could not,why is it so?
  14. P

    How to Integrate (x) sq. root of ((x^2) - 1)?

    (x) sq. root of ((x^2) - 1)?
  15. N

    Integrate sqrt ( 4 -x^2)dx

    Hi, Can anyone help me integrate : Integral sqrt ( 4 - x^2) dx Some ideas: Make a subsitution x2 = cos (theta) Taking the derivative of both sides: 2x = - sin (theta).d(theta) or... Double angle identity: (Cosx)^2 = 1 + cos2x / 2 Can anybody give some ideas.
  16. Y

    How to integrate sqrt( cos(x) + cos(x)^3)

    I need to integrate Sqrt[Cos(x)+(Cos(x))^3] Mathematica gives answer with AppelF, I've never heard about it. This excercize was given in my book, so there must be answer in elementary functions. I tryed 1) tg(x/2)=t and 2) Cosx=t , but both didn't help me. Give me please any advice. What does...
  17. T

    Integrate this without gauss theorem

    Hi guys, I want to solve this integral without using gauss theorem to convert from double to triple integral, my problem here is to find a general way for setting the differential surface part (ds) from the integral if \vec{F} was a vector field defined as: \vec{F} = x^3\vec{i} +...
  18. T

    How can Sine Integrals be calculated using polynomial representations?

    Hi guys, I think the question is clear (lol) How can the Sin(x)/(x) function be integrated? i heared it can be integrated using a series, anyone can explain? Last added : I remembered the function e^(x^2) how also can it be integrated? Thanks, TheDestroyer
  19. I

    How should I integrate this differential equation?

    How should I integrate this differential equation? dQ/dt = 10 - 10Q/(500 - 5t) I hope someone can help me.
  20. H

    Integrating sin(x^2) using substitution method

    how to integrate sin(x^2)?
  21. M

    How can you integrate a vector without decomposing it in x and y components?

    Hello, I just wanted to know if you can integrate a vector, and if so, how. Here is a problem: A charged piece of metal of linear density 2 * 10^-6 * x , between x=2 and x=5. I found its charge by integrating.. and it is 21 micro C. Now that's what I want to know: calculate the electric...
  22. A

    Integrate d/dx(x^2): Include Constant?

    if i integrate d/dx(x^2), should i include the constant of integration? thanks
  23. J

    I have no idea how to integrate by parts

    I don't think anyone in class understands it, we went over it so quick. The only thing I seem to get is that uv - (integral) vdu = (integral) udv. You are supposed to assign u, v, dv and du, but how do you know which is u and which is v? What is the difference between du and dv? Are you...
  24. S

    How Do You Integrate 1/(x(ln x)^2) with Respect to x?

    How to integrate this for x? integral calc(1/x*1/(In x)^2*dx)
  25. H

    Integrate this integral from 0 to x of e^(-t^2)

    someone please show me how to integrate this integral from 0 to x of e^(-t^2) Thanks
  26. O

    How do I integrate these 3 functions?

    :confused: How do I integrate these 3 functions? (1) \alpha(t-t_{0})=\int_{R_{0}}^{R(\Theta)}\frac{du}{u\sqrt{a^ 2-u^2}} (2) \beta(t-t_{0})=\int_{R_{0}}^{R(\Theta)}\frac{du}{u\sqrt{u^ 2+b}} (3) \beta(t-t_{0})=\int_{R_{0}}^{R(\Theta)}\frac{du}{u\sqrt{u^ 2-b}} A million thanks in...
  27. H

    Can Gamma Function be used to Integrate Factorials?

    By definite integral, gamma function can be defined as \Gamma(z)= \int_{0}^{\infty} t^{z-1}e^{-t} dt I've learned some properties of Gamma function but my lecturer didn't tell us the domain of Gamma function. (I'm assuming it is defined for all non-negative real numbers). I thought of...
  28. H

    Integrate e^x cos(x)dx, how to do this?

    Some one please show me how to do this problem below Integral of e^x cos(x) dx how to I integrate that? thanks
  29. F

    Could someone me simplify this so I can integrate it

    I have to integrate: sqrt( (3t^2)^2 + (1)^2 + (sqrt(6)t)^2 ) at the limits t=1 and t=3 I can't figure out how to simplify the problem so that I can do the integral. So far the farthest I've gotten is the obvious: sqrt( 9t^4 + 6t^2 + 1 ) now I am stuck.
  30. F

    How to Integrate 1/(1+2x+x^2) dx Without Getting Stumped

    In an exam i stumbled when i saw this q integrate: 1/(1+2x+x^2) dx help
  31. F

    How do you integrate (r^2-x^2)^(1/2) with a constant r?

    how would you integrate (r^2-x^2)^(1/2) where r is constant thanks peace
  32. N

    Integrate exp(-x^2), dx

    hi all, i've tried to solve this thing with Derive, but it gave me some vague erf(x) function (error function??). Is there some gosu-mathematician who can help me solve the integral? \int exp(-x^2) dx tnx
  33. E

    How do i integrate (cot(x))^2

    hi all, but how do i intergrate (cot(x))^2 thx
  34. tandoorichicken

    Integrating tan(3x) using substitution method?

    How do you integrate tan(3x)? As in \int \tan{3x} \,dx
  35. M

    How the heck do I integrate sin(1/x) ?

    I tried parts by integration but I am caught in an endless loop of ever growing in complexity integrals! I must be missing something.
  36. K

    How to Integrate by Parts Twice for e^3x cos(x)?

    I am studying for a midterm, was browsing over an old midterm and found this question \int e^{3x} \cos{(x)}\; dx Can't figure it out, help would be appreciated
  37. L

    Integrate cos^3xdx - First Clue: Substitute (1-(Sinx)^2)cosxdx

    Any suggestions on how to integrate \int cos^3xdx My first clue would be to substitute (1-(Sinx)^2)cosxdx but any clue to go after this?
  38. P

    What is Lonewolf's proposed method for integrating Ln[x]dx?

    Integrat Ln[x]dx!
  39. K

    How to integrate without trigonometric substitution

    S(x²(1-x²)¹/²)dx without use x=sen(T)? Sx^2(1-x^2)^1/2dx x=sen(t) dx=cos(t)dt (-pi/2<=t<=pi/2) S(x^2(1-x^2)^1/2)dx=S(sen^2(t)cos^2(t))dt S(sen^2(t)cos^2(t)^)dt=S((1-cos^2(2t))/4)dt =S1/4dt - S((co^2(2t))/4)dt= t + c1 - S((1-cos(4t))/8)dt =t/4 + c1 - S1/8dt + S(cos(4t)/8)dt= t/4 +...
  40. M

    What is the Integral of 2^(x)?

    Could someone please help me with the integral of 2^x. dx I bet its really simple but i have looked in several books and they just give the answer.
  41. C

    Integrate 1/(1+e^x) - Is it Correct?

    need to integrate 1/(1+e^x) by using th rule 1/(ax+b) = (1/a)ln(ax+b)+c i got (1/e^x)ln(1+e^x)+c that is correct is it not? because if i now differentiate that, i get 1/(1+e^x)..which is what we start with. I am damn sure this is right, but its causing some arguments.
  42. N

    Can erf(x) be used to solve e^(x^2)?

    does the integrate e^(x^2) can solve?? i think is no... but why??
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