#Integrals (3)

134 messages · Page 1 of 1 (latest)

gentle epoch
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I have an exercise to prepare for my exam on calculating integrals. I've tried several times to do it but I just can't do it. It's in French btw. Bounds x = -2 and 2 see attachment.

C07EBBBF-6F50-4D96-801E-7CD2E1E5F040.jpeg
weak steppeBOT
gentle epoch
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this is what I tried already but aint able to get the right answer (34/3)

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Ion get where I am wrong tbf

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<@&286206848099549185>

ivory aurora
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,w x^2+2x-3=0

sudden vortexBOT
ivory aurora
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,w integrate x^2+2x-3 from -2 to 1

sudden vortexBOT
ivory aurora
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,w integrate x^2+2x-3 from 1 to 2

sudden vortexBOT
ivory aurora
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this should be -9

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and this should be 7/3

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also an abuse of notation here, but I know that we're all a bit sloppy on the computer

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@gentle epoch

gentle epoch
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but this doesnt get me to 34/3 I think

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Or either I'm wrong on the final resolution

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bcs 34/3 is 11.33333

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But I have -9 and 2.33333

ivory aurora
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so the total area is just 9

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$9+\frac{7}{3}=\frac{34}{3}$

gentle epoch
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or since it's the air I get to -34/3 but i have to be pos. ?

sudden vortexBOT
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Civil Service Pigeon

560122149126275093.png
gentle epoch
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you're right

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thanks

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You might have an idea for the 2nd one or you're busy ?

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I can try something and send it here

ivory aurora
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it seems like the same idea

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so use the same logic you did

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try to avoid computational slips this time tho

gentle epoch
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yea sure

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Ion know where I lost some stuff in my resolution tho, has to be a calculation error

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,w integrate x^2+x from -1 to -1/2

sudden vortexBOT
gentle epoch
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,w integrate x^2+x from -1/2 to 2

sudden vortexBOT
gentle epoch
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I have this

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for the 4 =>

C07EBBBF-6F50-4D96-801E-7CD2E1E5F040.jpeg
ivory aurora
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$\int^{2}{-1/2} (2x+1) \dd{x}=[x^2+x]^{2}{-1/2}$

sudden vortexBOT
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Civil Service Pigeon

560122149126275093.png
gentle epoch
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I need to get the right f(x) nah?

ivory aurora
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??

gentle epoch
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I don't get it

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what's wrong

ivory aurora
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What is "the right f(x)" supposed to mean

gentle epoch
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I need to get to x^2+x

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right ?

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So I intergrated it

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Or either i didn't understood ur question

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might be my fault my main language's french so im trying my best

ivory aurora
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Tu as déjà intégré (2x+1) à (x^2+x)

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(Le français n'est pas ma langue maternelle, mais j'ai essayé) 🤷‍♂️

gentle epoch
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Sure no worries we can keep going in english tho i u prefer, but wym by am I integrating the antiderivative, like wheres the mistake

ivory aurora
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there's no reason to integrate x^2 + x

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it already came from integrating f

gentle epoch
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so what should i do ?

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this ? ,w integrate 2x + 1 from -1 to 2

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,w integrate 2x+1 from -1 to 1/2

sudden vortexBOT
ivory aurora
gentle epoch
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Oh sorry then

ivory aurora
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np

gentle epoch
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,w integrate 2x+1 from -1 to -1/2

sudden vortexBOT
gentle epoch
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,w integrate 2x+1 from -1/2 to 2

sudden vortexBOT
gentle epoch
# sudden vortex

and on the first one, did I had to integrate as I did or it had to stay like this

ivory aurora
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$\int^{1}{-2} (x^2+2x-3) \dd{x}=\left[\frac{1}{3} x^3+x^2-3x \right]^{1}{-2}$

sudden vortexBOT
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Civil Service Pigeon

560122149126275093.png
gentle epoch
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so this was right fine, just a calculator mistake

ivory aurora
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this is fine (barring the arithmetic mistakes)

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this had the same issue I mentioned earlier

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gentle epoch
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alright thanks, if u got time i just got two more, one that looks like these and one for the volumes

ivory aurora
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can you send a screenshot please

gentle epoch
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yea sure

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ion why they sent like that

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so the last one

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I need to find the air between the two functions

ivory aurora
gentle epoch
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on this one ion really know how should i do, should i do f(x)-g(x) ?

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and from 0 to 1

ivory aurora
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,w graph y=x+x^2, y=3x

sudden vortexBOT
ivory aurora
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but yeah, just integrate the difference

gentle epoch
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you're right

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like this ?

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ig

ivory aurora
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the line is above the curve so it should be $$\int^{2}{0} (3x) \dd{x}-\int^{2}{0} (x+x^2) \dd{x}$$

sudden vortexBOT
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Civil Service Pigeon

560122149126275093.png
ivory aurora
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don't forget the dx either

gentle epoch
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perfect

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lm try it and I'll see if i don't do any calculating mistake

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sounds good

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this the last one that I got

ivory aurora
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The idea is that when you rotate the curve, the solid you get has a bunch of circles as cross sections

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I’ll let you look up a visual of that yourself

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But the distance from the x axis to the curve is your radius

gentle epoch
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I've done this already ion know if its right

gentle epoch
ivory aurora
gentle epoch
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but since it starts at 1, shouldnt i start a 1 ?

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and yea the dx thanks

ivory aurora
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It’s a function of x, so you integrate over the values of x

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Also, if that were the case, your upper bound would be wrong then

gentle epoch
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so if I have somethinf like that at my exam I'll have to go from 0 to 2

ivory aurora
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Sure

gentle epoch
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ok

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so

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,w pi.integrate(x+1)^2 from 0 to 2

sudden vortexBOT
gentle epoch
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its this ?

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oh no

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forgot the radical

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,w pi.integrate(x^1/2+1)^2 from 0 to 2

sudden vortexBOT
gentle epoch
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thanks a lot man

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u might've saved me there

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good evening

weak steppeBOT
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gentle epoch
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