Question

Sorry...trouble with integration.
See below.

Answer 1

\[\int\limits (x^2+3)^{1/2} dx\]

Answer 2

so i know that u = x^2+3 so du = 2xdx and 1/2 du = xdx

Answer 3

Doesn't look like you're going to be able to find a home for your DU :(
Trig Subbbbbbbbb

Answer 4

my main question is what do i do with the x in front of the dx?
my thought is to solve for x in terms of u so that x = rad( u-3)

Answer 5

You certainly could do that, but you'll end up with an integral that is almost exactly the same in terms of U.

Answer 6

@zepdrix i haven't learned trig sub. i think

Answer 7

Hmm

Answer 8

theoretically you can divide by x, no? u^(-1/2)?

Answer 9

@Edutopia sorry can u explain?

Answer 10

well you divided by 2 didnt you..

Answer 11

yeah, but there's no x other that the u that i subed in.

Answer 12

The x is in the du that you input, there wasnt a 2 either before you created one

Answer 13

let me compute this to make sure im not telling you wrong :)

Answer 14

i took the derivative?

Answer 15

Woops I messed up my sub :3

Answer 16

oops, i forgot x =/= u lol

Answer 17

\[\large \int\limits\limits (u)^{1/2}( \; \frac{du}{2x}) \qquad \rightarrow \qquad \int\limits \frac{u^{1/2}}{2\sqrt{u-3}}du\]

Answer 18

@zepdrix that what i was thinking , but does it evaluate?

Answer 19

same here.

Answer 20

No I don't think so :D
Trig subbbbbb \:D/

Answer 21

sorry i don't know how to do that yet sorry...

Answer 22

are you sure there isnt another x in there some where?

Answer 23

nothing i forgot.

Answer 24

Aha!

Answer 25

\[\frac{ 1 }{ 2} \int\limits\limits u^{\frac{ 1 }{ 2 }} (u-3)^{\frac{ 1 }{ 2 }}du\]
i got to there...

Answer 26

yea you have to solve for x in your u sub, and then substitute that in

Answer 27

yeah, i simplified what i did up there and it's gonna take a lotta u subs to solve that.....
cuz i got 1/2 int (u^2-3U)^1/2 du

Answer 28

no its X^2 = u-3 i believe

Answer 29

which makes x = rad (u-3)

Answer 30

x = +- sqrt(u-3) not that that is helping

Answer 31

i just use positive

Answer 32

good thing, you may be right there

Answer 33

\[\int\limits (u^2-3u)^{\frac{ 1 }{ 2 }}du\]
i got this when i simplified it

Answer 34

what happend to the (1/2)

Answer 35

oh sorry i forgot to put it. but yes, it should be there.

Answer 36

i got ...

Answer 37

\[\int\limits_{}(1/2)\frac{(\sqrt{u} du)}{\sqrt{u-3}}\]

Answer 38

because you have to divide by x

Answer 39

do you know integration by parts?

Answer 40

@jennychan12 I believe at your newbie level, all you do is recognize the formula to plug in:
√ ( x² - a² ) = (1/2) x√ ( x² - a² ) + a² ln | x + √ ( x² - a² ) | + C
In your case a = √ 3

Answer 41

@Chlorophyll correct , i was about to suggest this

Answer 42

just wondering can u do trapezoidal rule?

Answer 43

@chlorophyll do you know what that process you just outlined is called, (i want to look it up)

Answer 44

It's from the appendix C of a Calculus textbook
section "Integrals involving √ ( x² - a² )

Answer 45

thank you

Answer 46

If I remember correct, the textbook title "Applied Calculus for Business, eco..."
by Raymond A Barnett and Michael R ..smth :/
( The book's too heavy so I just ... tore off the formula sheet for reference :P )

Answer 47

ok, so i tried using trapezoidal rule with 8 subintervals and i got 5.34825

Answer 48

\[\int\limits_{}^{}\sqrt{x ^{2}+3}dx\]Have you learned trig substitution?

Answer 49

no. but i used it i think once.

Answer 50

Well this would be your best option. Would you like me to explain and walk you through it?

Answer 51

This problem requires trig substitution.

Answer 52

In general:
\[\sqrt{a^2-b^2x^2} => x = \frac{ a }{ b } \sin(\theta)\]

Answer 53

@jennychan12 do you understand what I said? I am a teacher. I'll guide you through it and teach you, if you allow me.

Answer 54

oh i'm looking at my textbook and i'm getting confused. yes please.

Answer 55

but we don't actually learn it until next semester

Answer 56

OK. Do you understand what I wrote above: If given the expression\[\sqrt{x ^{2}+3}\]Substitute\[x =a \tan \theta\]if \[-\frac{ \pi }{ 2 }<\theta <\frac{ \pi }{ 2 }\]

Answer 57

sorry but why pick tan thetha? other than that, yes i understand it.

Answer 58

Because of the identity\[1+\tan ^{2}\theta =\sec ^{2}\theta\]

Answer 59

In our question\[a =\sqrt{3}\]Understand? Also, in the above explanation, it should be\[\sqrt{x ^{2}+a ^{2}}\]Typo!!!

Answer 60

sorry i'm new to this and might ask a lotta questions
why is a = rad 3? i thought it was 1?

Answer 61

lol 7 people

Answer 62

Given\[\int\limits_{}^{}\sqrt{x ^{2}+3}dx\]\[x =\sqrt{3}\tan \theta\]

Answer 63

Now tell me\[dx =?\]

Answer 64

@jennychan12 what is the derivative of √3tanθ, with respect to θ?

Answer 65

ohh √3(sec^2θ)

Answer 66

We're not doing u substitution! We are however, doing trig substitution!

Answer 67

sorry. i deleted that one.

Answer 68

Yes, so then if\[x =\sqrt{3}\tan \theta\]then\[dx =\sqrt{3}\sec ^{2}\theta d \theta\]Correct?

Answer 69

mhmm

Answer 70

Now do the substitution for x and dx in terms of θ.

Answer 71

@jennychan12 you're off answering other people's questions while I'm waiting for your reply. I don't appreciate that.

Answer 72

sorry. is it ok if i post this in another question? it's getting really long...

Answer 73

Sure but I don't want to type everything out from the beginning, so make sure you understood everything up to this point.

Answer 74

lemme type the question again so i don't have to scroll all the way up.
\[\int\limits_{1}^{3} (x^2+3)dx\]
i just forgot the limits at first.
okay so
just plug in x and dx right?

Answer 75

Woops your square root disappeared :O

Answer 76

sorry.
\[\int\limits_{1}^{3}(x^2+3)^{{ \frac{ 1 }{ 2 } }}dx\]