substitution

1. Calculating for position i in a series?

Hello. I have been trying to understand higher mathematical concepts, such as (I believe this is a series?). I have been trying to turn the following equation: x_{i+1}=rx_{i}(1-x_{i}) into a formula to predict position i of the equation, given both x_{1} and the inflation rate, r. Since I...
2. U-subsitution

Can someone please explain the u-substitution? I don't see a tan(x/2) anywhere in the integral expression.
3. Finding solution for natural logarithm equation

Hi, Can someone please explain to me why when solving for $2\ln{x} + \ln{x+2} - \ln{x^2 + 2x} = -\ln{2}$ the solutions for x are 0, 1/2, and -2,but when you substitute these values back into the equation, only x = 1/2 works? There may be some elementary concept relating to systems of...
4. Breaking apart a Denominator

This is a step in a current calculus problem am I attempting. This rewriting is essential to being able to solve the integral, but I am unsure how the author went between these two steps. To my knowledge, denominators cannot be broken apart. He seems to have moved a u to the outside and taken...
5. Trig substitution

Whitman 8.3.6 $\displaystyle I= \int x^2 \sqrt{1-x^2 } \ dx = \arcsin\left({x}\right)/8-\sin\left({4\arcsin\left({x}\right)}\right)/32+C$ As given by book answer. $$x=\sin\left({u}\right)\ \ \ dx=-\cos\left({u}\right) \ du$$ so then \displaystyle I=\int\sin^2 \left({u}\right) \cos^2...
6. Integral 1/sqrt(x^2+1) dx using Euler substitution

So I've seen some options on the internet, but I have this substitution x^2 + 1 = t^2-2tx+x^2 and you get x = (t^2-1)/2t, x + 1 = (t^2-1)/2t + 1 and if we call this function e(t) for example, dx is now equal to e(t) derivative. But how to proceed from here?
7. Simultaneous equation by substitution

Hi, I'm a GCSE Maths teacher in Leeds, West Yorkshire in England and am struggling to solve the following simultaneous equation by substitution to 2 dp: x2 + y2 = 9 and x + y = 2. Can anyone help? Thanks Laurence
8. System of equations : Solve with substitution

Hi I'm trying to solve this system of equations and cannot seem to get the right answer when i check it. Here are the two equations Using substitution to solve them, -3x-7y=1 2x+5y=9 So what i do for reference is set one of the equations to equal x then use that x in the other formula and...
9. Inverse Trig Substitution Integral help

I'm starting to get this, but I'm missing something on this one problem. I've tried so many different substitutions, but I can't get it to fit with any of my inverse trig functions. ∫1/[x(x^4-4)^1/2] any help would be awesome. Thanks in advance.
10. general solution of a 2nd order ODE using substitution

The question is, by making the transformation U=Xa Y where α is a constant to be found, findthe general solution of Y''+(2/x) y'+9y=0 I'm really struggling on this I've already subbed in the new values for Y but I then became stuck. I can see that it a variation of a Bessel Equation and tried...
11. Method Of Substitution with 3 variables.

Sorry for lack of intelligence if it doesn't meet the standards of this website, but I am only in grade 9 academic math, but I am pushing my territory further every day, while I was looking for puzzles online, I came across a puzzle for a 3D graph. This puzzle requires method of substituion...
12. TRIG SUBSTITUTION INTEGRAL- Where did I go wrong?

Imgur: The most awesome images on the Internet This imgur link shows my paper work and the solution manual to the problem I am trying to solve. My question is: how does the solution manual use "1/cos(x)" and end up with the integral of "cos(x)/sin^2(x)" whereas I use "sec(x)" and end up with...
13. Trigonometric Substitution

NOTE***In the image I wrote pythagorean theorem, it should be pythagorean identities.***NOTE Do I use the pythagorean identities or the rules for integrals involving sine and cosine for replacing cos^2(theta)?
14. Integration by substitution question

Click the image for my question.....
15. Trigonometric substitution

What can I do with cos2(theta)/sin2(theta) to integrate it?
16. Integral using trig substitution

Everything is fine, but the only difference between the right answer and my answer are the constants. I got 4/5 but they got 2/5. Also I haven't solved for C because If I did I would get the wrong C since my answer is wrong (4/5 instead of 2/5).
17. Integration by substitution

I understand all the steps until It was time for things to cancel. Written in red is my attempt in simplification. You can see that I have 125 as the constant but they got 5.
18. trigonometric substitution

The answer is pi/6 but I got 3. How did they get that?
19. Trigonometric Substitution

How did sec(theta) turn into sec^2(theta)? Also, why is sec^2(theta) being added to tan(theta)sec(theta). Didn't it say multiply?
20. U Substitution

For a homework problem, I have the integral: I got the answer (my work is in the file attached): But according to WolframAlpha, the answer shouldn't be negative and there should be an e in the denominator. I don't see why this is?