1. So I need to solve the following integral
∫1/(2+√x)
The Attempt at a Solution
By double integrating with u-substitution, I got to the following answer: 4+2√x-4ln(2+√x) + C
I can't find out where I go wrong, cause the answer is 2√x-4ln(2+√x), it has been a while, so maybe the...
Hello, I need help with a very hard integral, I was trying several steps and I tried in the software "derive" but the answer didn't like to me.
It is ψ(x,t)= [b^2-(x-vt)^2]^(-2) . I must integrate it with respect to x .
Thanks in advance for any help!
PD: I tried x-vt = u like the...
Homework Statement
A time-dependent torque given by a + bsin(ct) is applied to an object that's initially stationary but is free to rotate. Here a, b, and c are constants. Find an expression for the object's angular momentum as a function of time, assuming the torque is first applied at t =...
Homework Statement
Evaluate the following limits or determine that the limit does not exist.
b) lim (x,y)–>(0,0) (1+xy)^(1/xy)
Homework Equations
The Attempt at a Solution
I have a funny feeling this limit might exist. (Then again I get that feeling about every indefinite...
Is it possible to have a tank of water, run electricity through it, collect the hydrogen and oxygen, use it as fuel to heat the same tank of water into steam, use the steam to spin a turbine generating electricity to run through the water once more to create more hydrogen and oxygen to use as...
Hi I have not studied calculus for a while and I am just seeking some clarification on the following two problems I have attempted to solve.
PROBLEM 1
dy/dx = y(x^3 - √x)
I have separated the variables as follows:
Rewrote equation as dy/dx = y(x^3 - x^1/2)
Divided both sides by...
Homework Statement
\int (\frac{x}{\sqrt{x+8}}) dx
The Attempt at a Solution
I got to be honest, I don't even really know where to start with this problem. So bear with me as I take a wild stab in the dark. This section was substitution problems, ...
\frac{x}{\sqrt{x+8}} = \sqrt{...
Homework Statement
Consider the integral,
\int _3 ^7 (\frac{3}{x} + 2) dx
a) Find the Riemann Sum for this integral using right endpoints and n=4.
b) Find the Riemann Sum for this integral using left endpoints and n=4.
Homework Equations
The sum,
\sum^{n = 4} (\frac{3}{x} + 2)
The graph...
Homework Statement
Evaluate the integral
\int \frac{(a-x)^{r/s-1}}{(b-x)^{r/2}}dx
Homework Equations
given: s>r
The Attempt at a Solution
I tried using a substitution:
let u=b-x
so du=-dx
this gives:
-\int \frac{(a-b+u)^{r/s-1}}{u^{r/2}}du
I don't know what i should...
Homework Statement
The problem is divided into two sections:
a) does the improper integral: 2ln(x)/x^7 (from 1 to infinity) Converge or diverge? If it converges, to what value?
b) Determine whether the series: sigma n=1 to infinity (2ln(n)/n^7) converges or diverges.
Homework...
Homework Statement
\int (x+1)^2 dx
Homework Equations
The Attempt at a Solution
I am just getting into this, and this is a simple problem, but my book and I took two separate routes. My question, essentially, is does any constant you get just "combine" with the "any constant" C...
Homework Statement
A particle is moving with the given data. Find the position of the particle.
a(t)=t^{2}-4t+6,
s(0)=0,
s(1)=20
Homework Equations
The Attempt at a Solution
a(t)=t^{2}-4t+6, s(0)=0, s(1)=20
v(t)=\int t^{2}-4t+6 dt
v(t)=\frac{t^{3}}{3}-2t^{2}+6t+C_{1}
Then I suppose I take...
Homework Statement
I need help finding the anti-derivatives (indefinite integrals) of the 2 functions below:
1) e^(sqrt(x))
2) Sqrt(2x - x^2)
Homework Equations
The Attempt at a Solution
I tried forever at these 2 but I can't figure out a way for either of them. Any...
Homework Statement
\int \frac{\sqrt{x^4-1}}{x^3}dx
Homework Equations
The Attempt at a Solution
tried substituting x^4 = \sec^2 \theta to get rid of square root but it was of no use because, I got another complex integral \int \frac{\sin^2\theta}{\cos^{\frac{3}{4}}...
Anyone how to integrate this? Integration by parts doesn't get me anywhere, and there isn't a maclaurin series for ln(x).
Thanks!
(This isn't a homework question, I just was randomly doing integrals)
Homework Statement
S=integral symbol
S(5x+7)^28
Homework Equations
Substitution
The Attempt at a Solution
let u = 5x+7
du = 5
S u^28 du
= (u^29)/29 du
= [5(5x+7)^29]/29
is this correct? I'm not sure...
Homework Statement
\int{\sqrt{1+e^x}dx}
Homework Equations
\int{uv'}=uv-\int{u'v}
The Attempt at a Solution
I rewrote the integrand as
\sqrt{1+(e^{x/2})^2}
and used the trigonometric substituition e^{x/2}=tan(\theta), which simplified the radical to...
Hey, all.
Anyway, browsing the Internet a bit I found this integral:
\int \sqrt{1 + \frac{\ln x}{x}}dx
as a proposed problem in a compilation of maths problems, as an integral from the MATYC journal. I gave it to Mathematica and WolframAlpha and they weren't able to solve it...
Given an indefinite integral,
\int f(x) dx = F(x) + C,
I am having some problems in understanding what this indefinite integral "is". The RHS is clearly a function, but what is the LHS? Judging by the equals sign, it should also be a function, but seemingly it isn't because there's no...
I am continuing here the discussion of side issues from another thread, quoting a number of Careful's promotional posts for indefinite spaces, negative probabilities, and other unconventional ideas for a generalized quantum mechanics. (A Nevanlinna space is a vector space equipped with an...
Homework Statement
Evaluate the indefinite integral.
Homework Equations
I tried to use substitution.
The Attempt at a Solution
I'm not so good with using the LaTex codes...so I attached a file I made in Word.
Thanks in advance!
Homework Statement
indefinite integral 5\picos\pit
Homework Equations
The Attempt at a Solution
5\pi int cos\pit
Substitution Method
5\pi x sin (1/\pit
Homework Statement
(e^-x)/(1+e^-x)dx
Homework Equations
Integral of e^x function
The Attempt at a Solution
I am completely lost with the problem, the fact that it is e^-x and not e^x has me stupped as well as the division.
Homework Statement
integral 1/(x(sqrt(x^2 - 4)))
Homework Equations
I don't know if there are any "equations" for integrals...
The Attempt at a Solution
Int(1/(x(Sqrt(4(x^2 /4)-1)
Int(1/(2x(Sqrt((x^2 /4)-1)
1/2 int(1/(x(Sqrt((x /2)^2)-1)
U-sub
u=x/2
du=1/2 dx
2du= dx...
This question is bugging me
if an indefinite integral is of the form F(x) + C
stating that F(x) is an antiderivative of f(x) and since the derivative of a constant is 0 the collection of all of the anti derivatives are of the F(x) + C accounting for the fact any constant can be tagged to the...
I arrived at this problem while trying to find the length of a 3D http://en.wikipedia.org/wiki/Cubic_interpolation" .
Basically, I'm having to figure out how to integrate ((At4+Bt3+Ct2+Dt+E)1/2)dt
A,B,C,D, and E are constants which have to be plugged in after integration, I'm sorry to say...
This is really a full on homework question but it WILL help me to solve my homework... by helping me fully understand the integral.
So I am trying to understand exactly what the indefinte integral means?
heres my train of thought...
if our function F(x) = x2 then its derivative is F'(x)...
Homework Statement
\int \frac{cos x}{sin^2(x) - sin(x)-6}2. The attempt at a solution
I first tried factoring the denominator.
\int \frac{cos x}{(sin(x) -3)(sin(x)+2)}
The first thing that came to my mind was Partial Factoring but I don't think it would work in this case.Thanks in advance!
I am having much trouble with indefinite integrals - i get most of the basic theory behind them but as soon as i am confronted with a larger more complex question i get stuck too easily.
These questions are not for my homework, they are just practice for my test. Any hints, tips and general...
Hello,
I'm kind of stuck in this problem. I have to express the integral as a power series.
the integral of (e^x -1)/x
I thought about evaluating it as f(x)=(e^x -1)/x and treating it as a Taylor series is that correct? Could I have any other hints?
I would really appreciate it...
I have a third order, non-linear, homogeneous, constant coefficient ODE that I need to solve but have no idea how to do it. To make matters worse, one of the boundary conditions are indefinite. Here's the equation,
y''' + y*y'' - y'^2 + 1 = 0
and the BC's
y(0) = 0
y'(0) = 0
y'(\infty) =...
Homework Statement
integrate lnsqrt(t)/t , dt
Homework Equations
The Attempt at a Solution
This is the most i can come up with.
u = lnsqrt(t), so du = 1/(2sqrt(t))dt , so dt = 2du/sqrt(t)
Im stuck @ this point
Homework Statement
Please explain how to use the substitution rule in indefinite integrals. I am unable even to start the problem.
Homework Equations
The Attempt at a Solution
Homework Statement
∫cos(x)/sin^2(x)*dx
Homework Equations
The Attempt at a Solution
Based off my earlier question, where is my error please.
u=sinx du=cosx*dx
∫u^-1*du sin(x)^-1 1/sin(x) + C -or-csc(x) + C
Thanks
Homework Statement
∫cos(x)sin^6(x)*dx
Homework Equations
The Attempt at a Solution
u=sin(x) then du should be -cos(x) according to the integral tables?
-∫u^6*du = -u^7/7
-sin^7(x)/7+c yet my book and calculator tell me the answer is positive. How?
1/(4+3x^2) ?
I'm trying to use this integration formula to solve for this
du
----------
a^2+u^2
I know my a would be 2, but what would my u be? I tried u = 3x and du=3dx and du/3=dx
but (3x)^2 would be 9x^2
Homework Statement
The problem reads(from the 4th edition of Stewart Calculus "Concepts and Contexts" pg. 394 #17):
Evaluate the integral.
the indefinite integral of dx/x^2*sqrt(4-x^2)
so this would read out as "the indefinite integral of dx over x squared times the square root of 4 minus...
S x^2(e^((x^3)+1))
I know I have to use integration by parts, and I'm guessing I should find the derivative of e^((x^3)+1), but I really have no idea where to start...
Homework Statement
how to solve the integral of x^3 - 3x^2 + 4x -9 / x^2 + 3 dx
Homework Equations
using long division
The Attempt at a Solution
x^2 + 3 divided into x^3 - 3x^2 + 4x -9 I am not sure
Homework Statement
\int \frac {2+z^{-1}}{z^{2}} dz
The Attempt at a Solution
Let:
u = 2 +z^{-1}
du = -z^{-2} dz
dz = -z^{2} du
so now its
\int \frac {u}{z^{2}} (-z^{2}) du
\int \frac {(u)(-z^{2})}{z^{2}} du
\int (u)(-1) du
and then the...
Homework Statement
\int \frac {1}{\sqrt{x}(1+\sqrt{x})} dx
The Attempt at a Solution
So let
u = 1 + \sqrt{x}
then
du = \frac {1}{2}x^{-1/2} dx
So dx should be this:
dx = 2x^{1/2} du
right?
So now the Problem looks something like this:
\int \frac...
Homework Statement
Find:
\int \frac {-1}{x^{2}(1+\frac{1}{x})^{2}} dx
Homework Equations
Same as before:
\int f(u)du = F(g(x)) + C
The Attempt at a Solution
Let
u = 1 + \frac {1}{x}
then
du = -\frac{1}{x^{2}}
so
\frac {-1}{x^{2}(1+\frac{1}{x})^{2}}...