Integrate Definition and 642 Threads

Homework Statement Integrate: \frac{dy}{dx}=0 The attempt at a solution \int \frac{dy}{dx}=\int 0\,.dx The answer is: y=0 or y=0+A? This is the part which is confusing, as i know that integral of 0 is 0, but do i have to add a constant of integration??

Homework Statement Find \int e^{-2x}\tanh x\,dx The attempt at a solution \int e^{-2x}\tanh x\,dx \\=\int e^{-2x}\times \frac{e^x-e^{-x}}{e^x+e^{-x}}\,dx \\=\int \frac{e^{-x}-e^{-3x}}{e^x+e^{-x}}\,dx Then i have no idea how to proceed.

1. ∫∫∫E6xy dV, where E lies under the plane z = 1 + x + y Apparently according to a classmate, the limits are: -1≤x≤0, -1-x≤y≤0, and 0≤z≤ 1+x+y I know how to get z. But I am confused for y and x. To solve the limits of y, you would plug in 0 for z, getting y = -1 - x. But why is the...

Homework Statement \int \frac{dx}{x^2-a^2} Homework Equations The Attempt at a Solution I've reached the answer, \frac{1}{2a} ln |\frac{x-a}{x+a}| + C , using partial fractions, but my professor asks for the work using substitution. Now I know how to do this when there's a...

Does anyone know how to prove the following statement? I haven't messed with integrals for awhile and I have to say that I am kind of rusty on this. From initial attempts, it seems the integral on the left is not something you can integrate directly... Maybe Taylor Expansion of cos^2(x) would...

This question is from my calculus assignment but I apologize if it belongs on the a physics board regardless. Homework Statement A particle of mass m is attracted towards a fixed point 0 with a force inversely proportional to its instantaneous distance from 0. If a particle is released...

Homework Statement Prove that \int^{∞}_{-∞} exp(-(z-ia)2)dz = √∏ for all real a. Homework Equations The Attempt at a Solution If I use the substitution x = z-ia then dz = dx and if I use the limits x = -∞ to x = ∞ I get the correct answer. However, I do not know how to justify leaving the...

Homework Statement This was a multi-part problem using the Clausius-Clapeyron relation to calculate how much pressure needed to be put on an ice cube in order to have it melt at -1*C. Homework Equations Clausius-Clapeyron relation given by: \frac{dP}{dT}=\frac{L}{T\Delta V} The...

I'm doing homework where i have to find a function representation of the output signal from a simple op amp integrator circuit with a 4.7k resistor and a .01uf capacitor. I know I'm supposed to use the equation -1/rc * int vin(t) but the input is a square wave signal. I never learned how to...

Homework Statement How do you integrate this? x-ae-b/x, where a and b are some constants. The Attempt at a Solution I have tried this http://integrals.wolfram.com/index.jsp?expr=x+*+e^%28-1%2Fx%29&random=false Is there a closed form of this?

Homework Statement Find ∫e^x/ (1+e^2x). dx , with limits ln 2 & 0 given u= e^x Homework Equations The Attempt at a Solution u= e^x du/dx = e^x dx= du/e^x sub limits of ln2 & 0 → u Hence, limits 2 & 1 Therefore, ∫u* (1+e^2x)^-1* du/e^x = ∫ u/ (u + e^3x) = ∫...

I have a mixture of multivariate normal distributions, and I want to compute the integral with the first element of the input vector varying between specified limits, and the other elements varying from -infinity to +infinity. See attached pdf for equations. I've done it numerically but would...

Homework Statement The problem is about solving the homogenous differential equation (x2 + y2)dx + (x2 - xy)dy = 0 using substitution, in this case y=ux. This is the example they go through in the textbook (A First Course in Differentia Equations with Modeling Applications, 9th Edition, Zill...

Hi there. I came to join this forum to seek help, because I can't solve the following homework question: The solution to this can be split in 3 right? 1. the homogenous #1: Eq:= c*x' +k*x =0 Characteristic: c*r+k=0 --> r=-c/k Homogenious solution: y(x) = A*exp((-(c/k)*x)) initi...

Homework Statement Evaulate the following integral: 2*integral from r-b to r of h(x-r+b)b*sqrt(r2-x2) dx or a picture http://imgur.com/n2PUN Homework Equations The Attempt at a Solution Tried setting u = r^2-x^2, lost after a couple more steps. Nothing seems to cancel out smoothly. For the...

I need some help with this equation. ∫xdx/(e^(3x)) Can someone tell me how to get started?

integrate Sinh4(x) I have been struggling with this problem for a week. I know the answer because of wolfram but I cannot see how it gets it. Honestly, I can't even decide what to make my substitution as. I haven't really had problems with any other questions from our homework but this one and...

Homework Statement Find \int t\sin(t^2-1) The attempt at a solution I've used the method of integration by parts. Let U=t, then dU =1 Let dV=sin(t^2-1), then V=-\frac{cos(t^2-1)}{2t} Then, \int t\sin(t^2-1)=t.-\frac{cos(t^2-1)}{2t}- \int -\frac{cos(t^2-1)}{2t}.1 Again, i use the method of...

Homework Statement im not sure the elegant way to put it, i need to integrate this somehow (ie, throw over the dt and integrate each side) but that squared is really tripping me up. is there a trick i should be using? -g(cos(x))=r(dx/dt)^2 Homework Equations The Attempt at a...

Homework Statement \int\frac{\sqrt{16+x^{2}}}{x} Homework Equations The Attempt at a Solution set x=4tant dx=4sec^{2}t dt so after plugging in and using a quick trig identity I get: \int\frac{16(sec^{2}t)*4sec^{2}t dt}{4tant} Then after a quick cleanup: 16*\int...

Homework Statement Evaluate the indefinite integral. ∫sin(27t) (sec(cos 27t))^2 dt Homework Equations The Attempt at a Solution u = cos27t du = -27sin27t dx = du / -27sin27t ∫sin(27t)*(sec(u))^2 * (du/-27sin27t)(-1/27) ∫(sec(u))^2 du (-1/27)*tan(u) = (-1/27)*tan(cos27t) + C ? I am...

Hi, I'm currently studying for my PDE exam, but my fundamental calculus skills might not be the best. I typed my question into wolfram alpha (http://www.wolframalpha.com/input/?i=integrate+-exp%28%28s%5E2+-+t%5E2%29%2F2%29*%28f%27%28t%29+-+t*f%28t%29%29+dt) and the result is correct, but I...

Homework Statement Integrate: I(a,b) = \int^\infty_\infty exp(-1/2(ax^2+b/x^2)) dx given \int^\infty_\infty exp(1x^2/2) dx = \sqrt{2\pi} Homework Equations The suggested substitution is y = (\sqrt{a}x - \sqrt{b}/x)/2 The Attempt at a Solution The substitution gives...

I'm not posing this to be a forum troll or to insult the excellent ongoing work in Physics. It's a serious question based on the following: * Most of relativity and QM theory was completed within 20 years by a few dozen scientists. * Their tools were very primitive-not even electric...

Homework Statement What causes integration of V_{in} within an RC circuit?Homework Equations Z= R + X_C = R - j/(ωC) Z is the impedance of the circuit, j=(-1)^.5, ω is angular frequency, and C is the capacitance. The Attempt at a Solution I think integration is the capacitor's way of...

Hi. Ok, so I'm trying to understand the "navigation equations". n: frame traveling on Earth with vehicle. e: frame centered in earth, rotating with it. P: Position of vehicle center of gravity. v^{n}_{P/e} = (vn,ve,vd): velocity of P w.r.t to e-frame, expressed in n-frame. Normally...

\int \frac{x-3}{x^2+2x-5}dx How integrate this task? x^2+2x-5=0 D=24, so I can't get real root.

Homework Statement Integrate f(x,y) = e^{-(x^2 + y^2)} over the set A = \{ (x,y): x > 0, y > 0, x^2 + y^2 < a \} Homework Equations The Attempt at a Solution The polar coordinate transformation g(r,\theta) = (r cos\theta, r sin\theta) is a diffeomorphism from A to the...

Homework Statement Find \int\frac{\cos y}{\sqrt(a-y)}\,dy The attempt at a solution Let U = cos y and dV = \frac{1}{\sqrt(a-y)} I get: cosy.-2√(a-y) - 2∫√(a-y).siny.dy So, again, i use partial integration: Let U = siny and let dV = [-2(a-y)^(3/2)]/3 I get: siny.[-2(a-y)^(3/2)]/3...

Homework Statement Integrate \nabla^{2} (\frac{1}{|\underline{r} - \underline{r}'|}) over the volume of a sphere using the divergence theorem. Homework Equations \nabla^{2} (\frac{1}{|\underline{r} - \underline{r}'|}) = -4\pi\delta^{(3)}(\underline{r} - \underline{r}') (i.e. it's a...

Is it possible to have an solution to this sort of integral? And if not, why not? \int_0^\infty \frac{e^{-ax}}{e^{-bx}+e^{-cx}}dx Is a Taylor expansion the only way forward? Many thanks David

If volumetric charge distribution has spherical symmetry I want to find the trapped charge a in certain radius Why did not need to do an integral from 0 to R to all the electric fields inside the sphere but take only the external field(how gauss law says)? The Electric fiels is...

What is ∫sin(sin(x)) dx ? I was told that it was not an elementary function. Then what function is it?

It is easy to integrate the delta function of real variable. But when the argument of the delta function is complex, I get stuck. For example, how to calculate the integral below, where u is a complex constant: \int_{ - \infty }^{ + \infty } {f\left( x \right)\delta \left( {ux}...

\int_\alpha\frac{1}{z^2}dz I can't figure out how to integrate this over a closed circle which contains the origin on its interior. I'm assuming it is equal to 2πi; is there a way to apply Cauchy's Integral Theorem? If I set f(z)=1/z then that is not analytic on the interior, so I don't see...

My friends were discussing about this problem (which they made up themselves). ∫\frac{1}{x^{2}+25}dx^{2} They were substituting x^2 for y (x^{2}=y) and thus the answer would come to be log(y+25) that is log(x^{2}+25) I don't think this is the case , i guess that we would be...

Homework Statement [SIZE="4"][SIZE="5"]∫ 1 /( sin x + sec x) dx Homework Equations The Attempt at a Solution ∫ cos x / ( sin x + cos x ) style question Tried ∫ cos x / (sin x . cos x + 1) dx and uses sin 2x tried substitutions nothing seem to work

Homework Statement integrate modulus of xcos∏x within the limits -1 to 1/2 P.S I'm not allowed to use acaluculator so graphing and finding out the answer not possible Homework Equations it's using the property of definite integral ∫f(x) dx within the limit from a to b = ∫f(x) dx...

Homework Statement I believe this is intended to be a proof of the formula πrl, surface area of a cone. Homework Equations A complete volume of revolution gives you a cone - the height h is the x value on a graph, the radius r is the y value. The y intercept is zero, therefore y=r/hx ...

Can anyone just help me integrate this 2 times. (with maple or somekind math program, or hand). Need to see if my 2 solutions is correct. :approve:

Dear all, Someone could help me to understand how I can resolve the following equation : dV/dt= A V^2 + B V + C Where V :V(t), A(t), B(t), C(t) Is there any method or indications about this ? Thanks in advance, Indira

Homework Statement ∫etxx2e-x Homework Equations M(t) = etx f(x) dx The Attempt at a Solution I know the solution is -1/(t-3)3, however I'm having difficulty integrating the function. UV - ∫ V DU is extremely long and challenging, I'm wondering if there is a shortcut (i.e. quotient rule?)...

http://www.wolframalpha.com/input/?i=integrate+1%2F%28%28x-1%29+sqrt%28x^2-2x%2B5%29%29 I have this problem, but there's no solution for it although it's definitively the hardest (people who lack common sense shouldn't write manuals). So, I decided to use wolfram, but it doesn't really help...

Homework Statement integrate: r2*exp(i*k*r - r2/a2) from -infinity to +infinity (in terms of r) Homework Equations relevant integration table The Attempt at a Solution not sure what this function or the method to solve this function is called

Hi, I would like to calculate one integral. I just want to get primitive function, not definite integral. ∫ 1/(x^2+a) dx where a is real number and >0 I only found that ∫ 1/(x^2+1) dx , its arctan(x) + C, but i don't know how it is with different 'a' values. Thanks for help!

I'm trying to find the arc length and I'm able to get this far. But it's been a long time since I've done calculus so I forgot. 1 to 2∫ √(25+100t^2) I tried to do u = 25+100t^2, du = 200t dt, dt = 1/200 du, but it doesn't look right.

As you can see the function given is K/[(y2 + K)1.5] The integral of this equation with respect to dy is part of the explanation my textbook gives of finding electric field due to line of uniformly charged wire, where y of course is the variable length of the wire. Then it gives the integral...

Evaluate the integral over the contour C when: f(z) = 1/z and C = {z(t) = sin(t) + icos(t) | 0 <= t <= 2*pi} I know f(z) = 1/r*e^(-it) = 1/r(cos(t) + isin(t)). But, when I try to take the contour integral by integrating f[z(t)]*z'(t), I get really messy formulas ((1/r*cos(sin(t))...

Hey guys! I have absolutely no experience with integrals, but i find them interesting. I do know that they represent the area between the function and the x-axis, but not much else. I was wondering if anyone could give me a simple explanation of what an integral is and how to actually solve one...

Can anyone show me how to do this: \int_a^b \left[\frac {\sin x}{x}\right]^2 dx