What is U substitution: Definition and 54 Discussions
In calculus, integration by substitution, also known as u-substitution or change of variables, is a method for evaluating integrals and antiderivatives. It is the counterpart to the chain rule for differentiation, and can loosely be thought of as using the chain rule "backwards".
Evaluate ##\displaystyle\int_{0}^{3}\frac{x+3}{\sqrt{x^{3}+1}}dx+5##
W|A returned 11.7101
ok subst is probably just one way to solve this so
##u=x^{3}+1 \quad du= 3x^2##
Homework Statement
## \int {sin} \frac{\pi x} {L} dx ##Homework Equations
u substitution
The Attempt at a Solution
If i make ## u = \frac{\pi x} {L} ## and then derive u I get ## \frac {\pi}{L} ## yet the final solution has ## \frac {L}{\pi} ##
The final solution is ## \frac {L}{\pi} - cos...
Homework Statement
The first part of the question was to describe E the region within the sphere ##x^2 + y^2 + z^2 = 16## and above the paraboloid ##z=\frac{1}{6} (x^2+y^2)## using the three different coordinate systems.
For cartesian, I found ##4* \int_{0}^{\sqrt{12}} \int_{0}^{12-x^2}...
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...
Look, I was wondering if substituting the variable more than once is valid and hence the definite integral intervals change this way.
Consider the following integral (I'm working for finding the volume of a solid of revolution):
*\pi \int_{-3}^{5}3^{2}-(\sqrt{\frac{y+3}{2}}+1)^2dy
Personally I...
Homework Statement
Evaluate the integral of (x+1)5^(x+1)^2
Homework EquationsThe Attempt at a Solution
I set my u=(x+1) making du=1dx. This makes it u*5^u^2. I integrated the first u to be ((x+1)^2/2) however I don't know what to do with the 5^u^2
Homework Statement
Use the substitution ##u=\frac{\pi} {2}-x## evaluate the integral ##\int_0^\frac {\pi}{2} \frac {\sin x}{\cos x + \sin x}dx##.
Homework Equations
[/B]
##\cos (\frac {\pi}{2}-x)=\sin x##
The Attempt at a Solution
[/B]I start by plugging "u" into the equation making the...
Recently I started seeing integral calculus and right now we are covering the topic of the antiderivative. At first sign it was not very difficult, until we started seeing integral variable substitution. The problem starts right here:
Let's suppose that we have a function like this:
\int...
So I'm doing length of an arc in my calculus 1 class. After plugging everything in the arc length formula.
Now I have this complicated function to integrate. Square root of (16x^8+8x^4+1)/16x^4.
I took the denominator out of my square root and got 4x^2.
Now I take u=4x^2.
Du/2x =dx...
So I am pretty bad at u substitution.
I don't really get how to replace values with du or u.
Can you please give me tips on how to do u substitution well?
Thanks.
Homework Statement
∫2x√(2x-3) dx
Homework Equations
The Attempt at a Solution
u=2x
du=2 dx
1/2∫u√(u-3) du
Am I on the right track with this? I'm not really sure what to do next.
Hi, I'm working on a u substitution problem so that.
u = 3-x
so that
du = (-1) dx ,
or
(-1) du = dx .
With these equations you just switch content from one side to the other with no problems?
Thanks,
Tim
Homework Statement
∫(1/x^(2))(3+1/x)^(3)
Homework Equations
U substitution is the way to go here
The Attempt at a Solution
My problem is that I can't figure my du and what is next. I know which one it is but I don't know the reason for it.
u=3+1/x
du= I chose ln|x| first but...
1. ∫ 1/(2√(x+3)+x)
2. Not sure if I'm beginging this correctly or not but I get stuck.
3. Let u= √x+3 then u2 = x+3 2udu=dx dx=2√[(x+3)
Therefore: ∫1/u2-3 Not sure where to go from here?
The problem statement
Evaluate the indefinite integral
∫\frac{\sqrt{x}}{\sqrt{x}-3}dx
The attempt at a solution
My first thought was to substitute u for √(x)-3, but then du would equal \frac{1}{2\sqrt{x}}dx, and there's no multiple of du in the integrand.
Next, I tried splitting up...
Homework Statement
use the substitution u= x+y and v=y-2x to evaluate double integral from
∫1-0∫(1−x) -(0) of (√x+y) (y−2x)^2 dydx
Homework Equations
integration tables I am assuming
The Attempt at a Solution
i tried to integrate directly but none of my integration tables match...
∫(cot^4 x) (csc^4 x) dx
Wolfram wants to use the reduction formula, but I'm meant to do this just using identities and u substitution. I was thinking something along the lines of:
=∫cot^4 x (cot^2 x + 1)^2 dx
=∫cot^8 x + 2cot^6 x + cot^4 x dx
but I don't know where to go from there.
Homework Statement You know the U substitution proofs for inverse trig functions that go like this:
\int\frac{1}{a^{2}+x^{2}}dx
\int\frac{a\frac{1}{a}}{a(1+\frac{x^2}{a^2})}dx
let u = x/a
du= dx/a
...
\frac{1}{a}tan^{-1}(x/a)+cI have searched google and can't find any of these proofs for...
Homework Statement
∫3xdx/√(1-2x)
Homework Equations
The Attempt at a Solution
so i tried making u=3x which makes du=3dx but that substitution doesn't get rid of the x unde the square root. i tried u=1-2x and that gives du=-2dx and that doesn't get rid of the x on top. So I'm...
Homework Statement
Use Part 2 of the Fundamental Theorem of Calculus to find the derivative.
\int_3^x sin(t^{5}) \, dt Homework Equations
The Attempt at a Solution
I know the general idea of what I'm supposed to do as far as evaluate the indefinate integral and then do a subtraction of the...
Homework Statement
The Attempt at a Solution
if x2 = u - 1, and if x3 = x2 * x, then x3 should equal (u-1)x, not .5(u-1).
I'm assuming that they got u.5 because (x2+1).5 = (u-1+1).5 which is the same as u^.5
I would think because of this
The following problem:
At this stage they should use integration by parts:
However, maybe integration by parts is only useful when one of the parts is e^x ln or a trigonometric formula.
Homework Statement
find ∫x/√(x+1).dx with limits 1 & 0
using substitution x = u^2 -1
Homework Equations
The Attempt at a Solution
dx = du
x = u^2 -1
u = √( x+1)
sub limits of 1 & 0 into u.
Hence new limits of √2 & 1
Therefore,
∫ u^2 -1/ u
= ∫ u - 1/u
=...
Homework Statement
Find the integral of 3x* (2x-5)^6*dx, let u= 2x -5.
Homework Equations
Im not sure if i am meant to use integration by parts or not?? I was able to do previous questions of the topic just using u sub to get rid of the first x variable.
The Attempt at a Solution...
Homework Statement
make a u- substitution and integrate from u(a) to u(b)
Homework Equations
∫[0,1] √(t^5+2t) (5t^4+2) dt
The Attempt at a Solution
u= t^5+2t du= 5t^4+2
u(1)=2 u(0)=0
∫[0,1] √(u) du
(2/3)(u)^3/2+c l[0,2]
(2/3)( 0^5+2(0))^3/2- (2/3)(2^5+2(2))^3/2
0+...
Homework Statement
use substitution to evaluate the integral
Homework Equations
1)∫ tan(4x+2)dx
2)∫3(sin x)^-2 dx
The Attempt at a Solution
1) u= 4x+2 du= 4
(1/4)∫4 tan(4x+2) dx
∫(1/4)tan(4x+2)(4dx)
∫ (1/4) tanu du
(1/4)ln ltan(u)l +c
2) u=sinx du= cosx or u=x du = 1 ?
Homework Statement
\int_0^∞ x^2exp(-x/2) dx
Homework Equations
The Attempt at a Solution
Using u substitution:
u = x/2
du = 1/2 dx
\int_0^∞ 4u^2exp(-u) du*2
= 8 \Gamma(3)
= 8*3!
= 48
But the correct answer is 16 when I plug it in Wolfram's definite integral...
The problem: The definite integral of [(x^2sinx)/(1+x^6)]*dx on the interval -∏/2 ≤ x ≤ ∏/2
I need help figuring out what the u should be for substitution.
I've been trying to make the (1+x^6) my u, but I don't know if this is what I should be doing.
Homework Statement
Hi I am having a few problems with the below u substitution can anyone help,
In particular what to do with the integral of the u substitution?
Homework Equations
\int2x2 square root of 1-x3 dx, u = 1-x3
Any pointers would be appreciated
Thanks
D
I received no credit, resulting in an 84 for a few integral problems. I had correct final answers for everything.
When I confronted my professor about this, he said it was because I didn't actually put "u" and "du" into the integral. Is that really always necessary? Why actually put the u in...
Homework Statement
the integral of 1/(1-y)dy
Homework Equations
The Attempt at a Solution
ln|1-y|+C
however I believe you use u substitution as 1-y=U? Why is this so?
Homework Statement
Using substitution, find the integral of 32x2/(2x+1)3
Homework Equations
The Attempt at a Solution
I initially tried plugging u in for 32x2 but that wouldn't work because it won't cancel out with the problem below it anyway. I'm pretty sure we are not expected...
Homework Statement
integral of 1/(x^2 + z^2)^(3/2) dx,
where z is a constant
Homework Equations
The Attempt at a Solution
I set u = arctan(x/z) so du = z/(x^2 + z^2) dx but now I'm honestly stuck.
Homework Statement
Using the u substutituion u = 2x + 1, ∫(2x + 1)1/2dx (when x goes from 0 to 2) is equivalent to?
Answer: (1/2)*∫(u)1/2du (when x goes from 1 to 5)
Homework Equations
The Attempt at a Solution
If u is 2x + 1, then du = 2dx. Thus, I get
(1/2)*∫(u)1/2du...
Allow me to explain my new theory, The "Mancini conjecture."
Ok...lets say I have an integral like (4-x^2)^(1/2) dx.
and letting u = 4-x^2, we get du/dx = -2x,
and if I took the second derivative of du/dx...i would get -2
this would be ideal, because I would then have du'' = -2 dx, or -1/2...
Homework Statement
As I was reviewing some of my previuosly learned calculus I came across somthing that I had either forgoten how to do or was never taught. How do you take the integral of somthing like this
\int \sqrt{\frac{9}{4}x+1}
I don't know how to start with this one. Do I use U...
Hey,
I need to evaluate \int_{1}^{5}(6-2x)\sqrt{5-x}dx
So.
\tex{Let ~~u} = 6-2x~~ \tex{then}~~ du = 2
\frac{1}{2}~du = dx
New limits:
x = 5 \longrightarrow u = -4
x = 1 \longrightarrow u = 4
now, -\frac{1}{2}\int^{4}_{-4} u*\sqrt{5-x}
and now for the partial integration.
u \sqrt{5-x}~~ -...
Homework Statement
how do i integrate
v^2 / v^2 + 4
Homework Equations
i understand this has something to do with arctan
but if i use u substitution to let v=(u/2) so (on the bottom) it becomes (1/4)(1+(v/2)^2)
there's still a v^2 on the top which the u substitution does not...
Homework Statement
If a and b are positive numbers, show that \int_0^1 x^a*(1-x)^b\,dx = \int_0^1 x^b*(1-x)^a\,dx using only U substitution.Homework Equations
Just U substitution and the given equation--I can't use multiplication rules or anything like that; otherwise it would be easy.The...
Hi,
We were going over trigonometric integration in Calculus II the other day. I got the basic idea, but get lost when we're doing the u-substitution.
We had a problem like this:
\int cos^3 (x) dx
Then we did:
\int (1 - sin^2 (x)) cos(x) dx
Starting u-substitution:
u =...
so I'm having problems with the coefficients in this problem.
\int(10z+8/z^2-8z+41)dz
i know that the main chunk is
(a)ln|(z-4)^2+25|+(b)arctan((z-4)/5)
a and b are 5 and 32/5 respectively
the problem is i can't seem to split up the top so that the first portion is the derivitive...
Homework Statement
Find the indefinite integral.
The antiderivative or the integral of (x^2-1)/(x^2-1)^(1/2)dx
Homework Equations
The Attempt at a Solution
Tried using (x^2-1)^(1/2) as u and udu for dx and I solved for x but I am still left with a 1 on top not sure how to...