Indefinite Definition and 296 Threads

Now the steps to solution are clear to me...My interest is on the constant that was factored out i.e ##\frac{2}{\sqrt 3}##... the steps that were followed are; They multiplied each term by ##\dfrac{2}{\sqrt 3}## to realize, ##\dfrac{2}{\sqrt 3}\int \dfrac{dx}{\left[\dfrac{2}{\sqrt...

Will it be [{(r-a)/r}*H(r-a)]

I have the following integration - $$\int \frac{2}{x - b \frac{x^{m - n + 1}}{(-x + 1)^m}} \, dx $$ To solve this I did the following - $$\int \frac{1 - b \frac{x^{m - n}}{(-x + 1)^m}+1 + b \frac{x^{m - n}}{(-x + 1)^m}}{x(1 - b \frac{x^{m - n}}{(-x + 1)^m})} \, dx $$ Which gives me -...

$$x(t)=\int \dot{x}(t)\mathrm dt=vt+c$$ That's what I did. But, book says $$x(t)=\int \dot{x}(t)\mathrm dt=x_0+v_0 t+ \frac{F_0}{2m}t^2$$ Seems like, $$x_0 + \dfrac{a_0}{2}t^2$$ is constant. How to find constant is equal to what?

Hi When we find integrals of Bessel function we use recurrence relations. But this requires that we have the variable X raised to some power and multiplied with the function . But how about when we have Bessel function of first order and without multiplication? How should we integrate it ?

Since ##h## and ##k## are constants: $$\frac{h}{k}\cdot \int \frac{1}{y(h-y)} \ dy$$ Now, rewriting the integrating function in terms of coefficients ##A## and ##B##: $$\frac{1}{y(h-y)}=\frac{A}{y}+\frac{B}{h-y}\rightarrow B=A=\frac{1}{h} \rightarrow$$ $$\frac{1}{h}\int \frac{1}{y}\ dy +...

Hi guys, I got to solve this integral in a recent test, and literally I had no idea of where to start. I thought about substituting ##tan(\frac{x}{2})=t## in order to apply trigonometry parametric equations, integrating by parts, substituting, but I always found out I was just running in a...

That's my attempt: $$\int (\frac{1}{cos^2x\cdot tan^3x})dx = \int (\frac{1}{cos^2x}\cdot tan^{-3}x) dx$$ Now, being ##\frac{1}{cos^2x}## the derivative of ##tanx##, the integral gets: $$-\frac{1}{2tan^2x}+c$$ But there is something wrong... what?

I've tried with this work in attachment. i&m not sure of my answer is correct.

Let x=t^2 Then dx=2t dt Integral of 1/(x(1-x))^(1/2)dx = integral of 2tdt/t(1-t^2) ^(1/2) = integral of 2dt/(1-t^2) ^(1/2) = 2 arcsin(t) +c = 2 arcsin(rt(x)) +c. But the answer in my book is arcsin(2x-1) +c. Tell me how 2 arcsin(rt(x) +C= arcsin(2x-1) +c I know the constant will vary for both...

This is going to sound like a silly question, but here we go anyway! I've always thought about a definite integral being used for modelling a change in some quantity whilst an indefinite integral is employed to find the defining function of that quantity. For example, consider the...

Homework Statement The indefinite integral $$\int \, $$ and it's argument. The indefinite integral has a function of e.g ## \cos (x^2) \ ## or ## \ e^{tan (x)} \ ## If the argument of ## \cos (x^2) \ ## is ## \ x^2 \ ## then the argument of ## \ e^{tan(x)} \ ## is ## \ x \ ## or ## \ tan (x) \...

To help find the velocity of particles requires the evaluation of the indefinite integral of the acceleration function, a(t), i.e. v = Z a(t) dt. Your help greatly appreciated.

I was wandering if there is a way to understand whether it is possible to find an indefinite integral of a function. Let's say e^(-x^2) or e^(x^2)... They can't have indefinite integrals, but how can I say it? Is there a theorem or something?

Homework Statement Calculate the indefinite integral of the function ## \int\frac{3x^3}{\sqrt{1-x^2}}## my book gives the answer ##-(2+x^2)\sqrt{1-x^2}+C## Homework EquationsThe Attempt at a Solution So I started trying to calculate this indefinite integral by using a substitution...

Calculation of $\displaystyle \int e^x \cdot \frac{x^3-x+2}{(x^2+1)^2}dx$

First, just to check, I write what I think and let me know if I am wrong: The definite integral of a function gives us a number whose geometric meaning is the area under the curve between two limiting points. We can calculate this integral as the limit of the sum of the rectangles and the...

doubt in this fraction in here Because he, simplify 12 with 4 ?? do not understand! someone could make another example ,with fraction ! Thank you!

Homework Statement find the following integral: cos(x/2) - sin(3x/2) dxHomework Equations I think the substitution method has to be used. Solve integrals by parts. The Attempt at a Solution Let u = x/2 cosu du/dx=1/2, I then inverted it so dx/du = 2/1 = 2 So dx=2du Now I have cosu2du Do I...

F(x) = \int_a^x f(t) dt I have found various arguments online for both. Personally I think it's an indefinite integral because: 1) Its upper limit is a variable and not a constant, meaning the value of the integral actually varies with x. This is no different to the family of primitives...

Hello, Please can someone help me solve my problem. I have recently submitted my answer and had my work referred for an error. I have pictures of my question and working out, however i can not seem to post them on the page. can i email them to someone for advice/guidance Thanks

Upto how many levels of recursion can be used in an algorithm to avoid stack overflow error ?

micromass submitted a new PF Insights post Some Misconceptions on Indefinite Integrals Continue reading the Original PF Insights Post.

I have a calculator which allows me to sketch indefinite integrals - it assumes c = 0. However, when I try to use Desmos Online Graphing Calculator, it won't let me do this with it's integral function. It keeps trying to make me use definite integrals. I know that ∫(a,b,f(x)dx = F(a) - F(b), so...

What is the $\displaystyle \begin{align*} \int{ \frac{54\,t - 12}{\left( t- 9 \right) \left( t^2 - 2 \right) } \,\mathrm{d}t } \end{align*}$ We should use Partial Fractions to simplify the integrand. The denominator can be factorised further as $\displaystyle \begin{align*} \int{ \frac{54\,t -...

What is the indefinite integral (with respect to t) of $\displaystyle \begin{align*} 50\,t\cos{ \left( 5\,t^2 \right) } \end{align*}$? $\displaystyle \begin{align*} \int{ 50\,t\cos{\left( 5\,t^2 \right) } \,\mathrm{d}t } &= 5\int{ 10\,t\cos{ \left( 5\,t^2 \right) }\,\mathrm{d}t } \end{align*}$...

Not sure if the correct term is indefinite or undefined... I mean something like an infinite series that does not sum to a particular value, like this: X = 1 - 1 + 1 - 1 + 1 - 1 + 1... where pending the placement of parentheses one can infer multiple answers for X So, is it proper to say X...

Homework Statement Im looking over the notes in my lecture and the prof wrote, \int_{0}^{2} \pi(4x^2-x^4)dx=\frac{64\pi}{15} Im wondering what's the indefinite integral of this equation. Homework Equations using u substitution The Attempt at a Solution \int \pi(4x^2-x^4)dx= \pi \int...

Homework Statement ∫(sin2(πx)*cos5(πx))dx. Homework Equations Just the above. The Attempt at a Solution I have no idea how pi effects the answer, so I basically solved ∫(sin2(x)^cos5(x))dx. ∫(sin2(x)*cos4(x)*cos(x))dx ∫sin2(x)*(1-sin2(x))2*cos(x))dx U-substitution u = sin x du =...

Homework Statement ∫sinxcos(x/2)dx This isn't an actual homework problem, but one I found that I'm working on for test prep. Homework EquationsThe Attempt at a Solution [/B] ∫sinxcos(x/2) dx = ∫sinx√((1+cosx)/2) dx u = ½ + ½ cosx -2 du = sinx dx -2∫√(u) du = -2(2/3⋅u3/2) + c -2(2/3⋅u3/2)...

Hello forum, please take a look at the following picture: It's a salt solution, with increasing refractive index, as you go down the solution. How can I explain this with Fermat's principle? Let's set the starting point A to the point, where the laser beam penetrates the left wall of the...

Homework Statement Use the Fourier transform to compute \int_{-\infty}^\infty \frac{(x^2+2)^2}{(x^4+4)^2}dx Homework Equations The Plancherel Theorem ##||f||^2=\frac{1}{2\pi}||\hat f ||^2## for all ##f \in L^2##. We also have a table with the Fourier transform of some function, the ones of...

Homework Statement okay so the equation goes: ∫(x*sin2(x))/(x3-1) over the terminals: b= ∞ and a = 2 Homework Equations Various rules applying to the convergence or divergence of integrals such as the p-test, ratio test, squeeze test etc The Attempt at a Solution Okay so I have tried...

First of all, I'm new here, so please bear with me if the answer to my question can be found elsewhere, but I have been working a problem and searching for an answer for two weeks now without a complete solution. In Eisberg and Resnick chapter 5, problem 15, an essential part of the problem is...

So here is the problem: Find the anti-derivative of sec 3x(sec(3x) + tan(3x)) Now I have tried foiling it out, and I am stuck at the part where I need to anti-derive Sec(3x)Tan(3x). Any help/tips would be greatly appreciated.

Homework Statement Evaluate the Integral: ∫sin2x dx/(1+cos2x) Homework EquationsThe Attempt at a Solution I first broke the numerator up: ∫2sinxcosx dx /(1+cos2x) 2∫sinxcosx dx /(1+cos2x) Then I let u = cosx so that du = -sinx dx -2∫u du/(1+u2) And now I'm stuck. I thought about turning...

I have posted my attempt and the problem above. Please help! Thanks in advance!

Suppose ##f## is defined as follows: ##f(x) = 1## for all ##x ≠ 1##, ##f(1) = 10##. Is the indefinite integral (or the most general antiderivative) of ##f## defined at ##x = 1##? I'm asking this question because I already know how to deal with, say, ##\int_0^2 f##; ##f## has only one removable...

Homework Statement Evaluate ∫e-θcos2θ dθ Homework Equations Integration by parts formula ∫udv = uv -∫vdu The Attempt at a Solution So in calc II we just started integration by parts and I'm doing one of the assignment problems. I know I need to do the integration by parts twice, but I've hit...

Just for fun, I tried this rather trivial problem, but I think I went wrong somewhere: $$\int arcsec(x) \ dx$$ Let ##arcsec(x)=y## . Then ##x=sec \ y##, or ##y=arccos(\frac 1{x})## So the problem becomes $$\int arccos(\frac 1 {x}) \ dx$$ Let ##\frac 1 {x} = cos \ u## , so that ##dx = secu \ tanu...

Homework Statement Find the indefnite integral using trig substitution. ∫[(x^2) / (1+x^2)]dx Homework Equations --- The Attempt at a Solution

1. http://www.imageurlhost.com/images/cnj1t05jh6e4fxqy4i5_integral.png I know that this integral is solved by the sustitution method The Attempt at a Solution I tried converting the integral to the form of Arctanx, but that x2 on the numerator ruined everything. Thanks

Look to this indefinite integral →∫e^(sin(x))dx Antiderivative or integral could not be found.and impossible to solve. Look to this definite integral ∫e^(sin(x))dx (Upper bound is π and Lower bound is zero)=?? my question is : can we find any solution for this integral (definite integral) ??

$\int\frac{1}{\sqrt{2+3y^2}}dy$ $u=\sqrt{3/2}\tan\left({\theta}\right)$ I continued but it went south..

I've been contributing to an open source calculator, and I wanted a way to take integrals of functions. I suppose you could implement a definite integral function by using Riemann Sums, but I can't find any way to implement indefinite integrals (or derivatives for that matter). I've heard that...

Let ##(M,g)## be an ##n##-dimensional pseudo-Riemannian manifold of signature ##(n_+, n_-)## and define the Levi-Civita symbol via $$\varepsilon_{i_1 \dots i_n} \, \theta^{i_1 \dots i_n} = n! \, \theta^{[1 \dots n]} = \theta^1 \wedge \dots \wedge \theta^n$$ where ##\theta^1, \dots, \theta^n##...

Evaluation of Indefinite Integral $\displaystyle \int_{0}^{1} \sqrt{1-2\sqrt{x-x^2}}dx$ $\bf{My\; Try::}$ We can write the given Integral as $\displaystyle \int_{0}^{1}\sqrt{\left(\sqrt{x}\right)^2+\left(\sqrt{1-x}\right)^2-2\sqrt{x}\cdot \sqrt{1-x}}dx$ So Integral Convert into...

$$\int_{}^{} \frac{1}{\sqrt{16+4x-2x^2}}\,dx$$ $$\frac{\sqrt{2}} {2}\int_{}^{} \cos\left(\frac{x-1}{3}\right)\,dx$$ So far ? Not sure

$$\int_{}^{} \frac{e^{2x}}{e^{2x}-2}dx. \\u=e^{2x}-2\\du=e^{2x}$$ Now what?

Evaluation of $$\displaystyle \int\frac{5x^3+3x-1}{(x^3+3x+1)^3}dx$$$\bf{My\;Try::}$ Let $\displaystyle f(x) = \frac{ax+b}{(x^3+3x+1)^2}.$ Now Diff. both side w. r to $x\;,$ We Get$\displaystyle \Rightarrow f'(x) = \left\{\frac{(x^3+3x+1)^2\cdot a-2\cdot (x^3+3x+1)\cdot (3x^2+3)\cdot...