/sci/ - Science & Math

Integrate both sides
dP/P = dt
My solution was
ln|P| + C = t + C

However, that's incorrect, the solution is
ln|P| = t + C
What happened to the constant on the left side?

This question is related to exponential growth/decay.

uh bump i just want some practice resources for basic integration

I haven't had any calculus. Can someone teach me how to integrate? Is there some universal foolproof way to do it like the quadratic formula?

there´s something that concerns me about Integrals, i hope you can help me out on that:

1. f(x) = (3x-2)^2
F(x) = integral (f(x))

i can build F(x) in two ways:

1.1. solving the binom:
F(x) = integral (9x^2-12x+4)
F(x) = 3x^3 - 6x^2 + 4x + C

1.2. substitution:
3x-2 = z, dz/dx = 3, dx = dz/3
F(z) = integral ((z^2)/3)
F(z) = (z^3)/9 + C
F(x) = ((3x-2)^3)/9 +C
F(x) = 3x^3 - 6x^2 + 4x - 8/9 + C

so:
1.1: F(x) = 3x^3 - 6x^2 + 4x + C
1.2. F(x) = 3x^3 - 6x^2 + 4x + 8/9 + C
if you compare them then you could say just let the 8/9 float into C i assume, but still what is now the legit answer:

F(x) = 3x^3 - 6x^2 + 4x + C
or
F(x) = ((3x-2)^3)/9 +C
or both of them?

Because I wasn´t sure i put it in http://www.wolframalpha.com/
and F(x) = 3x^3 - 6x^2 + 4x + C showed up (way 1.1)


then i did a second function:
2. f(x) = (x+3)^3
F(x) = integral (f(x))

I did it on both ways again:

2.1. (solving binom first):
Result: F(x) = (x^4)/4 + 3x^3 + 13,5x^2 + 27x + C

2.2 (substitution: x + 3 = z):
Result: F(x) = ((x+3)^4)/4 + C
-> F(x) = (x^4)/4 + 3x^3 +13,5x^2 + 27x + 20,25 + C

now i went to www.wolframalpha.com again and expected it to give me the solution 2.1 just like with 1.1, but this time it gave me the solution 2.2:
F(x) = ((x+3)^4)/4 + C

because it gave me both solutions on different occasions i wonder if they both are valid?
Please help me out on that one.

if you would change any symbol in mathematics, what would it be? and why?

Can someone help me with an integral exercise?

I have to calculate the volume of a function y=2sin(x/3)
Between the points 7 and 3pi

can someone do this step by step please?

I got my integral:

7S(3pi) pi . (2sin(x/3))^2 dx

(Don't know how I should formulate the integral, just to be clear the 7 is point a and 3pi is point b. The S is supposed to be the integral symbol)

Pic related.

Like the one out of the million sci/ientist there are, I am teaching my self calculus and I've understood everything so far using Spivaks Calculus, I just a have quick question regarding an example of the product rule.

Given f(x) = x sin(x)
f'(x) = sin(x) + x cos(x)
How do I get from that to this
f''(x) = -x sinx +2 cosx

I used the wolframalpha step by step solution and it is not clear to me still, maybe I'm not reading it as slow as I should be, but could someone just explain to me how that happened and the reasoning behind it. Thanks.

Can someone refresh me on calculus? When there's an integral of e raised to one variable but the integral is for another variable, how do I handle this?

/sci/, I'm in my 2nd semester of calculus, and I'm having problems understanding the solving logic behind integrals. Very basic integrals. I have this problem simply because in my head i'm not "finding the integral", I'm more of trying to find out what derivative gives me that integral.

Is this how it always is? Will I eventually not have to think twice about doing integration? I'm not really getting tripped up on any problems, but It's frustrating to have to use my understanding of derivatives and go in the opposite direction, as opposed to forward in the direction of integration, if that makes sense.

any tips or tricks? or just "Do more problems"(tm)?

hey guys, wolframalpha has failed me.
is there a technic for solving this kind of integral,
0-80 definite integral F(x) dx,
where f(x) is, lets say 30t-16
and x is 5t^3-8t^2-44t

thanks in advance, i can explain better if i couldnt write well enough!

hey /sci/
how would you integrate (2x^2 +1 ) / (x^2+1)^2 ?
tried separateing counter to x^2 +1 and x^2 so i had 2 fractions but the first one x^2 / (x^2 +1 ) ^2 seems cumbersome, its hard to split into partial fractions. any ideas / tricks?

thx

sup /sci/
how would you integrate x* 1/(1+x) ?

tried partially and failed... but it should work i don't know whats whit this

Calculus question. Currently in math class we are doing integration and shit and im wondering if there are a better way to do these. This is a pretty basic one but the methods should be the same, find the indefinite integral of csc^2(x)/cot^3(x). We are being taught to take find the u and right the equation in terms of u(du) then integrate ezpz and then replace the u with the actual term. so in this one u is cot so it would be u^-3(du) integrate that shit and get (u^-2)/2 replace u with cot and the answer is (cot^-2)/2. my question is if there is anyway to find what to call u in a more mathematical way because im basically just looking for something that looks like it could be u and i dont like it. how do i know the u is not csc.

Hey /sci/
simple question:
What's the integral of x?

Can you please explain integral calculus to me? Just the basics would be fine. Thanks.

What mathematical notation would you remove/change/introduce?

So I've been re-learning calculus with the intent of actually understanding it (instead of just memorizing formulas and methods for a test) and I can't quite figure out what things like "dx" mean exactly. I've heard that "dx" is an infinitesimally small increment of x, but then when I was reading about u-substitution, "du" is used in place of the derivative of u. So which is it? Is dx a very small change in x, or is it the derivative of x?

Integral thread! Show me some cool integrals.

Well, It's my first time on Sci and there doesn't seem to be a sticky about it's rules so please don't be too harsh if this is frowned upon.

I need a hint to begin my integration homeworks. I just don't know how to begin.

The equations are:
∫ from Pi/2 to Pi of (cos²(x)sin³(x)dx)
and
∫(sin(3x)cos(5x)dx)

How should I begin these problems?
(PS: I do not want the actual answers, all I want is a few hints to lead me in the right directions. Thank you very much!)

Show me your best integrals /sci/.

Hey guys, I have a really really dumb question about integrals. I know that dx/x = ln |x|, why is that though?

Hey guys, I derped and missed the first integration practice of my basic calculus course.

I know how to integrate by parts, but in the homework we are asked to solve the basic integrals without that or substitution, so, I have no idea.

integrate x^2dx/(1+x)

thanks in advance guys!

>That feel when you write your first integral

Hey /sci/,
I'm looking for an online calculator to calculate the average value of a function since I'm too cheap to buy a TI.