Indefinite Definition and 296 Threads

Homework Statement 2. The attempt at a solution I

Homework Statement 2. The attempt at a solution I integrated the velocity equation and got this: s(t)= sin(t) + (1/2)x 1. [sin(pi)+(1/2)(pi)] - [sin(0)+(1/2)(0)] = pi/2 2. [sin(pi)+(1/2)(pi)] + [sin(0)+(1/2)(0)] = pi/2 The first answer is right but the second one isn't

Homework Statement Integrate: ((e^arccos(x))(dx))/(sqrt(1-x^2)) Image of the question is attached. Homework Equations The Attempt at a Solution I think i took the right first step for substitution: u=arccos(x); cos(u)=x; (du)(-sin(u))=dx Substituting u into the...

Homework Statement Compute the following integral: Homework Equations none The Attempt at a Solution x^(1/2)-2(x^2)^(1/3) +1*x^(-1/4)dx = (2/3)x^(3/2)-...I don't know this part...+x * (4/3)x^(3/4) and this is where I stopped... btw sorry I didn't put the symbols and...

Homework Statement I need to evaluate the following integral: \int_{-\infty}^{\infty}x^mx^ne^{-x^2}dx I need the result to construct the first 5 Hermite polynomials. Homework Equations The Attempt at a Solution First I tried arbitrary values for "m" and "n". I was not able to...

Homework Statement \int_1^\infty \! \frac{(sin(x)+5)}{x^3} \, dx "Find two simpler integrals, one larger and one smaller." Homework Equations The Attempt at a Solution How could I make this a simpler (ie, solvable) integral? It's been straight forward with other integrals like...

Homework Statement \int \frac{ \tan x \sec^2 x }{ \tan^2 x + 6 \tan x + 8 } dx Homework Equations The Attempt at a Solution \int \frac{ \tan x \sec^2 x }{ \tan^2 x + 6 \tan x + 8 } dx Okay I let... u=tanx du=sec^2x Then I got \int \frac{ u }{ (u+4)(u+2) } du Then...

Homework Statement I hope someone can help me with this integral. It is really an improper integral, but I cannot figure out how to do the indefinite integral on it: integral[e1/x/x3]. Any help would be appreciated, thanks. Homework Equations ? The Attempt at a Solution I...

1. Homework Statement [/b] \int e^{3x}\sqrt{1+e^{2x}dx Homework Equations Substitution Parts of Integration The Attempt at a Solution Started off using U substitution setting ex = to u. Then tried to use parts of integration. Now I am stuck.

Nevermind, it's late and I realized why it doesn't work because I forgot to take into consideration that the denominator is (1/polynomial) Anyone care to explain to me how to do it the proper way? [SIZE="1"] 1. Question 1 \int (x+2)/(x²+x+1) dx The only reason I ask is because my...

Hey, I just need you guys to help verify that I got the correct answers on some of the even integration problems in my book. If one of them is incorrect, I'll post my work and hopefully can find out where I went wrong. Thanks! 1. \int xcos(x^{2})dx = \frac{1}{2} sin(x^{2}) +C 2. \int...

Homework Statement Find the indefinite integral of 16x^2+36+1/(16x^2+36) with respect to x Homework Equations Anything possible to take an anti-derivative The Attempt at a Solution I have absolutely no idea on how to deal with this problem. I can take an anti-derivative of the...

Hi, Looking to integrate the indefinite integral: \int tan~x\cdot ln~x\cdot cos~x Since tan x = sin x/ cos x, this integral be written as \int sin~x\cdot ln~x In that case i thought the answer was cot x. But that is wrong. Do you need to use integration by parts on this one?

Homework Statement \int{ x^3 \sqrt{(36-x^2)}dx} Homework Equations The Attempt at a Solution I tried using trig substitution but got 7776\int{cos^3(\theta)-cos^5(\theta)d\theta} which seems completely wrong 6cos(\theta)=x 6sin(\theta)d\theta=dx...

Hi, I missed a few days of my calculus class. I've managed to figure out how to use substitution to solve an indefinite integral, and can apply the log properties to some extent. I just can't figure out this problem. Homework Statement Find the indefinite integral: \int{\frac{1}{x...

Using U-substitution find the indefinite integral of: [sin(2x)/cos^4(2x)] dx So I do know that it will have to come out to it being ln... here's what i did so far ok so i made u= cos^4(2x) du= -8cos^3(2x)*sin(2x)dx...(just took the derivative of u and simplified it) so made sin(2x)dx=...

In a book while doing an indefinite integral the author first wrote (sec2 x)1/2 = |sec x| , fine , then the author says the following : "since we are doing an indefinite integral we can drop the absolute value bars" , now what is the justification for this ?

Homework Statement Evaluate the indefinite integral. \int \left({\sqrt[5]{x^5}}-\frac{6}{5 x}+\frac{1}{4 x^{7}} \right) dx The Attempt at a Solution O.k. the only anti-derivative I am having trouble getting is the first one {\sqrt[5]{x^5}}. I am not sure what formula I would use...

I have a system that ideally creates a real symmetric negative definite matrix. However, due to the implementation of the algorithm and/or finite-precision of floating point, the matrix comes out indefinite. For example, in a 2700 square matrix, four eigenvalues are positive, the rest are...

Hi, Our professor has only taught us these methods for Integration...thus far: Direct Integration Substituion Method So theoretically we should be able to solve these problems by substitution, direct integration...(double substitution) & by algebraic manipulation etc. Ive attached 3...

Homework Statement Hi, Our professor has only taught us these methods for Integration...thus far: Direct Integration Substituion Method So theoretically we should be able to solve this problem without using Integration by parts or partial fractions...: Integrate...

Homework Statement Solve the indefinite integral Homework Equations \int\frac{dy}{y(1-y)} How do I best approach this problem? I have been stuck for hours!

Homework Statement Hello, first of all I would like to apologize for the fact that this question is extremely trivial compared to the other questions being asked. I have a improper integral problem, and the entire problem itself is not relevant, because I understand everything in it except...

From a paper I've been reading: I wanted to know how to interpret the notation. What does it mean to take the derivative of u when it is a function argument? How do I take the integral wrt x of a seemingly-constant expression and not end up with x in the answer? Generally, how are these...

Homework Statement ∫(exp(6x))/(exp(12x)+25)dx Homework Equations answer: -arctan[5/exp(6*x)]/30 The Attempt at a Solution honestly, don't know where to start. i was looking at another forum and tried to set u=exp(x) du=exp(x) and dx=du/u. plugging that in i got u^6/(u^12+25)*du/u. not sure...

Homework Statement I'm looking at integrals about the unit circle and need to show that they equal 0. integral[e^zdz/(z-2)] integral(sinz/zdz) integral[sinhz/(z^2+2z+2)dz] My thoughts on showing these is using series. Is this the right idea? Also I'm looking at a couple of...

The world has been working more and more over the years to research a way to live indefinitely with health. What ways can you think of that biology can make an indefinite life span for a human? Of course, I am not looking for a sure fire way, I am just looking for brainstorms and ideas.

Homework Statement My daughter at college asked me to help her with these but it's been years since I've done them. I said I would try and then look over what she comes up with so any help would be great not so I can give her the answers but so I can tell her whether or not she on the right...

I have a very basic question regarding the nucleus. I understand why you can only have a limited number of protons within the nucleus - more and more protons within the nucleus will increase the coulomb potential and cause the nucleus to be unstable. But why is this so for neutrons? Why...

Homework Statement Find the average distance to the x-axis for points in the region bounded by the x-axis and the graph of y = x - x^2. Homework Equations The Attempt at a Solution Can someone guide me how to solve this?

Homework Statement Indefinite integral: e^(4x+(e^4x)) Homework Equations I'm thinking integration by parts, involving UV minus integral of Vdu The Attempt at a Solution So I saw that this can be split into two: e^(4x) times e^(e^4x)). The latter is a bit complicated. I...

Homework Statement If {\vec{V}(t) is a vector function of t , find the indefinite integral: \int (\vec{V}\times \frac{d^2\vec{V}}{dt^2}) \,dt Homework Equations The Attempt at a Solution I have solved it by decomposing and integrating each terms of vector \vec{V}\times \frac{d^2t}{dt^2}...

Homework Statement I wasn't really sure where to post this, as I don't need help understanding the integration. I need help with the trigonometry! That being said, here is the problem. Find the general indefinite integral of \int\frac{\sin{x}}{1-sin^2{x}}dx Homework Equations...

Find \displaystyle\int\dfrac{\sec ^2\sqrt{x}}{\sqrt{x}} dx We're supposed to use u du substitution but I can't seem to get this one. EDIT: Sorry I didn't read rules. I tried u=\sec^2\sqrt{x} and all variants. Usually it was in the form of [sec or cos][^2 or none][sqrt x]

A long time since i posted at physics forums. Anyways, try helping me solve the following integral \int\frac{1}{x^{2n} + 1}dx I tried many ways but all futile. The best way with which i could come up was factorising the denominator by de moivre's theorem. By finding the 2nth roots of...

Homework Statement 1. The calculation of the probability of excitation of an atom originally in the ground state to an excited state, involves the contour integral INTEGRAL(-INF TO +INF) [S exp(iwt)/(t2 + s2)2dt Evaluate the above integral. Homework Equations The Attempt at a...

Homework Statement Evaluate the following indefinite integral: (2t6-3)/t3 dt The Attempt at a Solution I know I need to substitute. Tried u= t3 and found du= 3t2dt. Tried to find where du would substitute in, but found...

Homework Statement Evaluate the following definite integrals using the Fundamental Theorem of Calculus: 1. 1 \int 4 ( (5x2+7x+5)dx ) 2. -5pi/6 \int 4pi/6 (−6sinx+7cosx) dx ) 3. 2 \int 4 ( (e^-4x)/((e^(-4x))+7) dx ) If it's unclear, the number on the...

Hey everybody, One question that I've had for a week or so now is how the following integral can equal a Dirac delta function: \frac{1}{2\pi} \int_{-\infty}^{\infty}{dt} \:e^{i(\omega - \omega^{'})t}\: = \: \delta(\omega - \omega^{'}) A text that I was reading discusses Fourier transforms...

Hi, I was wondering if a function is absolutely convergent over a certain interval, say, (0,\infty) will its indefinite integral also be absolutely convergent over the same interval? Also, assume that f(x) is convergent for (0,\infty). Would g(x) = \int{\int_{0}^{\infty}f(x)dx}dy &=&...

Evaluate this indefinite integreal S = integral S 1/(9+x^2)^2 This has been driving me and my friend nuts. We tried partial fractions only to realize that it brings us back to the same thing because its not a polynomial over a polynomial, we tried by parts and it did not help and we...

Homework Statement Find the constant, c, that satisfies the following equation: Homework Equations The integral is from -infinity to infinity 1 = c \int e ^ -|x|/2 *dx The Attempt at a Solution c = 1/4 I have the solution given to me, but I do not understand how to get the...

Homework Statement \int sinx/(1+cos^{2}x)dx Can anyone help me with this problem?

Homework Statement evaluate the integral ∫x^2 sinpi x dx Homework Equations ∫u dv= uv - ∫v du integration by parts formula The Attempt at a Solution u=x^2 dv= sin pi x dx du = 2x v = -cos pi x dx ? the pi is giving me trouble

of sin pi x dx i thought it would be - cos pi x dx but i think it might be (1/pi) -cos pi x dx

Homework Statement \int2e^-^7^xdx Homework Equations None The Attempt at a Solution (\frac{-2}{7})(\frac{e^-^7^x}{-7})+C This is as far as I can go, but the answer is: \frac{-2e^-^7^x}{7}+C

The integral of [sin^3*(13x)*cos^8*(13x)]dx I think u=sin^3 so du/dx=cos^3 du=cos^3dx but then I am really not sure if that is correct, the trig functions confuse me a bit. Please help me, thank you!

Evaluate the indefinite integral: [(e^(4x))/(e^(8x))+9]dx -I think that u=e^(2x) so then du=e^(2x)dx then the answer would end up being [(e^(4x)+9)/(-1)]^(-1) but it was incorrect; I think that my u might be wrong and that's where the problem is, but I am not sure. Please help, thank...

Homework Statement The integral of 5*(sin(6x)/sin(3x))dx The Attempt at a Solution I'm not quite sure what to do with this one. I moved 5 to the left of the integral, but then I'm lost. Apparently I'm rusty on these trig identities. Could anyone help me get started? Thank you.

Homework Statement Evaluate \oint x^2 (1-x^3)^6 dx Homework Equations The Attempt at a Solution let u= 1-x^3 du= -3x^2 -1/3 du= x^2 dx -1/3 \oint (u)^6 = -1/3 (u^7/7) = -1/21 (1-x^3)^7 + C Is this done correct? I think I followed all the right steps but there is...