Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing

This Question is Closed

abz_tech Group TitleBest ResponseYou've already chosen the best response.0
\[\int\limits_{3/2}^{1/2} dx/4x^{2}+12x+13\]
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.3
complete the square in the denominator and then trig substitute
 2 years ago

abz_tech Group TitleBest ResponseYou've already chosen the best response.0
i tried that but.. got stuck at the +13
 2 years ago

abz_tech Group TitleBest ResponseYou've already chosen the best response.0
got \[(x+2)^{2}+8\]
 2 years ago

abz_tech Group TitleBest ResponseYou've already chosen the best response.0
8 is not a square and if u factorise (x+2)^2 u dont get 4x^2....
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.3
factor that four out of the denom first\[\int_{\frac32}^{\frac12}\frac{dx}{4x^2+12x+13}=\frac14\int_{\frac32}^{\frac12}\frac{dx}{x^2+3x+\frac{13}4}\]\[=\frac14\int_{\frac32}^{\frac12}\frac{dx}{x^2+3x+\frac94+1}\]
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.3
\[=\frac14\int_{\frac32}^{\frac12}{dx\over(x+\frac32)^2+1}\]
 2 years ago

abz_tech Group TitleBest ResponseYou've already chosen the best response.0
how did u get 9/4+1? =/
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.3
13/4=(9/4)+1 completing the square on x^2+3x means adding a term of 9/4 you can save some trouble by noticing that 13/4=1+9/4 so we can make our constant term from the fraction we already have
 2 years ago

abz_tech Group TitleBest ResponseYou've already chosen the best response.0
can u continue plz
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.3
trig sub:\[x+\frac32=\tan\theta\implies dx=\sec^2\theta d\theta\]change bounds...
 2 years ago

dpaInc Group TitleBest ResponseYou've already chosen the best response.1
dw:1338250956092:dw
 2 years ago

abz_tech Group TitleBest ResponseYou've already chosen the best response.0
to be honest i just want to know how my teacher got dx/4x^2+12x+13 to be dx/(2x+3)^2+2^2
 2 years ago

abz_tech Group TitleBest ResponseYou've already chosen the best response.0
\[4x ^{2}+12x+13 \to (2x+3)^{2}+2^2\] can u tell me how he got it =/..thx
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.3
complete the square\[4x^2+12x+13=4x^2+12x+9+4=(2x+3)^2+2^2\]knowing that splitting the terms up like this is not as obvious as the way in which I did it I think, so it requires a little more intuition I prefer to get the coefficient of the x term to be 1 to be safe, but notice that you can take my answer and your teachers result follows if you let the 4 back in the denom
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.3
he just noticed that splitting the 13=9+4 would work
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.3
above I derived it my way\[=\frac14\int_{\frac32}^{\frac12}\frac{dx}{x^2+3x+\frac94+1}\]let back in the 4 now...\[=\int_{\frac32}^{\frac12}\frac{dx}{4x^2+12x+9+4}\]from whence follows your teacher's way note both will give the same answer obviously
 2 years ago

abz_tech Group TitleBest ResponseYou've already chosen the best response.0
alright thx.. but the way u did is not in my course =/ i dont even know what changing bounds means..yet lol
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.3
the bounds in terms of x are 3/2 and 1/2 we make the substitution \[2x+3=2\tan\theta\]plug in the bounds of x and we can get them in terms of theta\[2(\frac32)+3=0=2\tan\theta\implies \theta=0\]\[2(\frac12)+3=2=2\tan\theta\implies\theta=\tan^{1}1=\frac{\sqrt2}2\]so the new bounds are\[\int_{0}^{\frac{\sqrt2}2}\text{(whatever)}dx\]
 2 years ago

abz_tech Group TitleBest ResponseYou've already chosen the best response.0
:o..never did that.. before :P..kinda confusing.. we jsut call what u call bounds..limits
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.3
whatever floats your boat I just don't like getting that term confused with limits like\[\lim_{x\to a}f(x)\]
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.3
call 'em Freddies for all I care though, makes no mathematical difference whatever is easiest for you to keep straight
 2 years ago

abz_tech Group TitleBest ResponseYou've already chosen the best response.0
lol.. ya i guess, thx again see u around
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.3
welcome, good luck :)
 2 years ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.