What is Integrate: Definition and 650 Discussions

Happy new year for you all, This is very nice place, So girls and boys, let me give you something to play with: Integrate (r^.a)(r^.b)(r^.c)(r^.d) d(cos8) from cos8=1 to cos8=-1. a,b,c and d are constant vectors, r^ is the unit vector (iX+jY+kZ)/|r|, 8 is the spherical angle between r^...

may i know how to integ [2x sin (x^2) dx]??the answer is -cos(x^2) thanx...

Integrate (x^2 / sinx) / (1 + x^6): How to do this? I just need some clues...

When you intergrate a Ln ax problem does is the answer always 1/x for example integrate ln 2x does it equal 1/x or ln 3x and so on For some reason when i work it out on paper or my calculator it comes out to 1/x and I just don't think its right. I think I am just being catious since...

using "primitives" to integrate moments of Inertia My classmates are lost and I just can't think the way my proffessor does when approaching these problems. He gave us about 50 shapes to find moments of inertia for this weekend and I'm not having any trouble doing them... my way. I can use a...

Ok so I have to find the arc length from t=1 to t=2. \begin{array}{l} L = \int_a^b {|r'(t)|dt} \\ |r'(t)| = \frac{{2(1 + 2t^4 )}}{{t^3 }} \\ \end{array} And I have completely forgotten how to integrate fractions... Oh wait... i THINK i know what to do. Should i set u=1+2t^4?

Is it possible to integrate \int {cos (x^2)} dx ? If so, which method do I have to use?

Hi. I want to integrate x/(x^2 + ax + a^2) I tried substitution with u=x^2 then du =2x but that didn't work out neither did the substitution x^2 + ax I thought of factorizing the denominator and using partial fractions, but I think that's not the way, can't figure out the factorization...

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...

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...

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

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 =...

\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?

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:

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)...

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...

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...

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...

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

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...

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

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

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.

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...

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} +...

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

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

how to integrate sin(x^2)?

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...

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

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...

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

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

: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...

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...

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

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.

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

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

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

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

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

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

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

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?

Integrat Ln[x]dx!

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 +...

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.

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.

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