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onegirl
Group Title
Determine whether the integral converges or diverges. Find the value of the integral if it converges.
 one year ago
 one year ago
onegirl Group Title
Determine whether the integral converges or diverges. Find the value of the integral if it converges.
 one year ago
 one year ago

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onegirl Group TitleBest ResponseYou've already chosen the best response.1
@Reaper534 can u help?
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
Let's just focus on the integral first, keeping in mind that... \[\Large \int\limits_1^\infty x^{\frac43}= \lim_{b\rightarrow\infty}\int\limits_1^bx^{\frac43}\]
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
Well, can you integrate \[\Large \int x ^{\frac43}=\color{red}?\]
 one year ago

onegirl Group TitleBest ResponseYou've already chosen the best response.1
yes i get 3/3sqrt(x)
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
This \[\Large \frac{3}{3\sqrt{x}}\]?
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
Or this \[\Large \frac{3}{\sqrt[3]x}\]
 one year ago

onegirl Group TitleBest ResponseYou've already chosen the best response.1
the second one
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
lol... it's cube root, not 3sqrt because \(\Large3\sqrt x\) means something entirely different, ok?
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
Okay, so, we have... \[\Large \int\limits_1^b x^{\frac43}=\left.\frac{3}{\sqrt[3]x}\right]_1^b\]
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
Can you evaluate this bit?
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
Well then, what do you get?
 one year ago

onegirl Group TitleBest ResponseYou've already chosen the best response.1
hmm i'm working on it
 one year ago

onegirl Group TitleBest ResponseYou've already chosen the best response.1
eh...i'm getting a wrong answer :/
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
Fundamental theorem of Calculus? \[\Large \int\limits_a^b f'(x)dx = \left.f(x)\right]_a^b = f(b)f(a)\]
 one year ago

onegirl Group TitleBest ResponseYou've already chosen the best response.1
ohhhh okay
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
So... \[\Large \int\limits_1^b x^{\frac43} \ dx=\left.\frac{3}{\sqrt[3]x}\right]_1^b=\color{red}?\]
 one year ago

onegirl Group TitleBest ResponseYou've already chosen the best response.1
so i plug in b and 1 into that then subtract?
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
Yes... but that's not the end yet, just plug in for now, and tell me what you get :)
 one year ago

onegirl Group TitleBest ResponseYou've already chosen the best response.1
okay so 3/3sqrt(b)  3/3sqrt(1)
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
I'm assuming by 3sqrt you mean cube root :D Okay, that being the case, you're right :) \[\Large \int\limits_1^b x^{\frac43}=\frac{3}{\sqrt[3]b}+\frac3{\sqrt[3]1}= \frac3{\sqrt[3]b}+3\] Catch me so far?
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
Now, we're supposed to take the improper integral to infinity, right? Remember this... \[\Large \int\limits_1^\infty x^{\frac43} \ dx = \color{red}{\lim_{b\rightarrow\infty}}\int\limits_1^bx^{\frac43} \ dx\] Now is the time to apply that limit (which we haven't done yet) \[\Large \color{red}{\lim_{b\rightarrow\infty}}\left(\frac3{\sqrt[3]b}+3\right) \]
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
So... evaluating the limit...?
 one year ago

onegirl Group TitleBest ResponseYou've already chosen the best response.1
umm i get 3? :/
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
That's right!
 one year ago

onegirl Group TitleBest ResponseYou've already chosen the best response.1
ohh okay lol
 one year ago

onegirl Group TitleBest ResponseYou've already chosen the best response.1
so thats the final answer?
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
Well, you technically have two questions, but since there was an answer, then the integral converges, and it converges to 3 ^.^
 one year ago

onegirl Group TitleBest ResponseYou've already chosen the best response.1
okay thanks
 one year ago

terenzreignz Group TitleBest ResponseYou've already chosen the best response.1
No problem :)
 one year ago
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