Substitution Definition and 797 Threads

On this physics problem i need to do a double integral (dx,dy) of 1/sqrt(x^2 + y^2 +z^2). Which looks easy enough at first, until I reallized (after many hours) I cannot figure out how to integrate it. I am sure at this point there is some trig substitution (learned too long ago...), but I am...

When is th ebest time to use it and what are some good rules of thumb for it?

calc/integral question having trouble with this question int[1/((x^2+4)^2) and i make a trig substitution x=2tan(u) and it seems to get harder with that but its suppose to be it..

Yes, it's me and the wave packets... again! This is taken from the text of Gasiorowicz's Quantum Physics 3rd ed. pp.26. We have a gaussian wave packet at t=0 that is is described by \psi(x,0)=\int_{-\infty}^{\infty}dke^{-\alpha (k-k_0)^2/2}e^{ikx} and we apply the change of variable...

Let f: \Re^3 \rightarrow \Re be differentiable. Making the substitution x = \rho \cos{\theta} \sin{\phi}, y = \rho \sin{\theta} \sin{\phi}, z = \rho \cos{\phi} (spherical coordinates) into f(x,y,z), compute (partially) df/d(rho), df/d(theta), and df/d(phi) in terms of df/dx, df/dy...

Integral Substitution... Heya people, I was wondering if someone here could point me in the right direction, as the book I am reading on Integration isn't very thourough, and I don't really have anyone else to ask. :confused: Basically, I am reading up on u-substitiution regarding...

Hi, I have another problem about substitution Method. I think this method is used to make the problem to solve in easy way but it is making my procedure too long for this problem. Can you solve it by substitution method. S (x+5)½/x-4 dx where S is the sign of integral. The answer of...

I'm trying to find the antiderivative of [sec(2x)tan(2x)], I can't figure out what part I should be substituting. Any help is appreciated. Thanks, hk

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...

hi guys im debating whether this question requires trignometric substitution or just normal substitution. ∫ √9-2(x-1)² Im leaning towards normal substitution, with u = x-1, but I am not sure Any ideas Thanx heaps

how can i integrate: x^2+7x+10 dx x+2 i assume it's by substitution, but i can't work it out. sorry for the formatting, btw

Hello everyone I have an exam tomorrow and I would really appreciate if someone could tell me what I did wrong with this exercice. I did it on paper and I scanned it. Here is the link to the scan: The answer in the book is sqrt(x^2 + x +5/4) + 2ln(sqrt(x^2 + 2x + 2) + x +1) + C...

Hello everyone, I am having some trouble with an integral. \int \sqrt{x^2 - 1} dx so far: x = sec \theta \frac{dx}{d \theta} = sec \theta tan \theta dx = sec \theta tan \theta d\theta now we substitute: \int \sqrt{x^2 - 1} dx = \int \sqrt{sec^2 \theta - 1} sec \theta tan...

im hoping i worked this out right; its long: \int x(81-x^2)^{5/2}dx the integral contains a^2-x^2, so i set x=asin\theta. that would make x=9sin\theta and dx=9cos\theta d\theta: \int 9sin\theta(81-81sin^2\theta)^{5/2}9cos\theta d\theta = \int 9sin\theta[81(1-sin^2\theta)]^{5/2}9cos\theta...

Using the Substitution method, find the maximum value of 4x-2xy+3y subject to the constraint 4x-y=2 I can do the 1st part: 4x-y=2---> 4x-2=y substitute this into the original equation: 4x-2x(4x-2)+3(4x-2) Hope that right so far! but don't know where to go from there? anyone...

Hi, I'm new to the forum, and new to differential equations. I was wondering if someone could post a no-nonsence explanation of substitution methods for first order differential equations. Thanks!

i don't understand when to use substitution as used in the answer to this question: how fast must a pion be moving, on average, to travel 10m before it decays? average lifetime is 2.6*10^-8. i know the answer is D=V( to/ sqroot 1-v^2/c^2) but i don't understand why and how to know when...

\int x^3\sqrt{4-9x^2}dx I tried to use x=\frac{2}{3}\cos{(x)} but it just left me with \int \sin^3{(x)}\cos^2{(x)}dx Any suggestions? Thanks for your help.

Use trig substitution to find \int_{0}^{5} \frac{dt}{25 + x^2}dt I can solve it to here \int_{0}^{\frac{\pi}{4}}\frac{25sec^2\theta}{(25 + tan^2\theta)^2} and from this point i can factor the denominator into {625(1+ \tan^2\theta)}^2 which becomes 625\sec^4\theta now i have the...

Hi, I have to find this one: \int \frac{dx}{\sqrt{1-e^{2x}}} Is this right approach? \int \frac{dx}{\sqrt{1-e^{2x}}} = \int \frac{e^{2x} dx}{e^{2x} \sqrt{1-e^{2x}}} Substitution: t = \sqrt{1-e^{2x}} dt = - \frac{e^{2x}}{\sqrt{1-e^{2x}}} dx e^{2x} = 1 -...

The question is Evaluate the double integral over the region R of the function f(x,y)=(x/y -y/x), where R is in the first quadrant, bounded by the curves xy=1, xy=3, x^2 -y^2 =1, x^2-y^2 =4. Now it seems that a substitution would be the best bet. What I've done is make u=xy, and v=x^2...

I am going crazy on this problem: \int sec(v+(\pi/2)) tan(v+\pi/2)) dv if I substitute u= tan(v+\pi/2)) dv , can I use the product rule to find du= sec(v+(\pi/2)) dv . Thanks, Todd

can someone help me find a appropriate trig sub for this problem: \int\frac{x}{sqrt(-29-4x^2-24x)} took out sqrt(4)... sqrt(4)*sqrt(-29/4-x^2-6x) (i also changed all the negative signs to positive) complete the square... sqrt(4)*sqrt((x+3)^2-7/4) so my trig sub should be...

\int \frac{1}{4x+7*sqrt(x)} what would be a good u substituion for this problem? i can't think of any at the moment

\int \frac {cos(\sqrt{x})}{\sqrt{x}}dx =? Here's what I did: = \int x^{-0.5}cosx^{0.5}dx subsitute: u= cos(\sqrt{x}) du=-sin(\sqrt{x})(0.5x^{-0.5})dx -\frac {1}{0.5sin(\sqrt{x})}\int u du -\frac{2}{sin(\sqrt{x})} 0.5cos^2(\sqrt{x}) -\frac{1}{sin(\sqrt{x})}cos^2(\sqrt{x}) I know I...

The NO2 group directs meta with-deactivation in electrophilic aromatic substitution. The nitroso group - NO directs ortho-para with - deactivation. Write out the electroinc structures of - NO2 and -NO and explain the differences in behavior. Show all pertinent resonance forms for the addition of...

Consider the definite integral \int \frac{(x^3)}{(sqrt(3x^2-1))} can someone help me find the appropriate subsitution? i know that i will need this subsitution: sqrt(x^2-a^2) is equal to x=a*sec(theta) well... i have to make 3x^2 look like x^2 somehow. i tried using u-du sub...

for carbanions, for carbocations and for carbon-centred radicals, does increasing the number of alkyl substituents stabilise or destabilise the intermediate? and why so? :confused: :confused:

Use subs y=xv to show that (x^2+y^2)+2xy\frac{dy}{dx}=0, x>0 is x^3+3xy^2=k where k is a constant. I played around with this at school and if memory serves me correct i got something similar to \frac{dx}{dv}=\frac{-3}{2xv}-\frac{1}{2} and after that i decided i wasnt on the right path and...

Hi guys, could someone just suggest a variable substitution for me...just to get the ball rolling : \int_{-1}^{1} \sqrt{1-x^2} - x^2 (\sqrt{1-x^2}) - (1-x^2)^\frac{3}{2} dx Whenever I've seen \sqrt{1-x^2} (and its usually the reciprocal of), I've used trig substitutions to wind...

How would you go about solving \int \frac{\sqrt{1-x^2}}{x^2} ? I have tried a few things... drawing out triangles... etc but can't seem to get it... I am kind of behind in math because I was gone for awhile because of being sick and presentations.

I'm stuck on how to advance further on this problem and if anyone can point my in the right direction I would be greatly appreciative. \int\frac{dx}{\sqrt{x(1-x)}} The integral has to be solved using substitution, but we are required to use u=\sqrt{x} From this...

Integration by substitution... Accroding to my notes, when performing integration by substitution, du/dx= f'(x), and therefore du = f'(x)*dx. But how is this possible? We are treatnig dy/dx as if it were a fraction - but in essence it is not! So why is this statement still true? Thanks. :smile:

hey guys i recently found a code in a spam e-mail sent to me, it apears to be a word substitution code and i haven't been able to break it (not sure if there is a way) anyway here's the portin of code i got, if you think you might need more examples e-mail me, i won't post them here becasue some...

Hi all, I'm totaly lost on how to get started on this one. Integrate 1dx/(x^(1/2)(1-x)^(1/2)) The solution manual jumps right through the substitution and ends up as Integrate (2u*du)/(u(1-u^2)^(1/2)) I'm just not seeing it, little help please. Keith

the problem is shown in the picture i attached. wouldnt i use u = 2sec(\theta) as a sub?

Please help. I'm having trouble with a simple integration by substitution problem The integrand is f(x) = x* sqr(x-1) The interval [1,2] Please draw it out in a gif file and send it to me via email. -much appreciated.

hi guys, i need to calculate the substitution resistance between the points A and B of the chain in the attached picture. Each rectangle is a resistance R , except the resistance on the right-top of the figure. That has value 2R ; and the solution has to be (13/11)R. I know that we have to...

Hi, I'm currently stuck on an integration via substitution problem. I have an answer but the one given in the book of the book is different to mine. I'm wondering where exactly I've gone wrong, if i have: Q10: Integrate: x/ (x+1)^0.5 dx. Use the substitution, u^2 = x + 1. Heres my...

How do I evaluate: d/dt sqrt [ t^4 + t^2 ]= 0 to get a max/min value. can I make a u substitution of some sort?

Hello, everyone... I am new to OOP, and this is the first time I make a question on PF, hope you can help me out. I am not sure about this principle. Can you tell me in what ways I can *break* Liskov substitution principle ? Thanks, ~Alek

If this equation is true: V=(V1+V2)/(1+(V1*V2)/c^2) Then why is it when you plug in c^2 for both V1 and V2 you get the total velocity as 2m/s

\int\frac{dx}{x^4+1} What really frustrates me is that I've seen this integral before. I believe it involved some whacky subsitution like x=e^u, but no substitution seems to work. Partial fractions just make a mess. Trig subs seem tempting but that 4 screws everything up. Ideas?

For our homework this week for Pure, one of the questions is to ingration 1/(16 + x^2) with respect to x between the limits 0 and 4. I know the result from the formula wqith arctan in it, but since we've to use substitituion here and not just plonk down the formula, I'm confused as to what to...

At the moment I'm trying to solve this integration problem and it's not working out asd neatly as any other substituion problem I've tried before. We have to integrate sqrtx divided by (1 + x^2) using the substitution x= tan^2t (as in tan squared t). So when we have dx/dt so you get...

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 +...

How do you do this question, I've spent hours figuring it out: Use the substitution x = 3sint to show that 3 [inte]x^2[squ](9-x^2) dx = (81/16)pi 0