idk what i got wring here

[tawny scaffold]

question wants to evaluate the interval by using the definition of the integral.
i did it here but for some reason it doesnt add up any idea why?

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[prisma summit]

I would suggest you break it down to multiple simple steps

first of all, due to linearity, you can easily see that what you need to calculate is:
$$4 \int_{-1}^{2} x^2dx + \int_{-1}^{2} x dx + \int_{-1}^{2} 1 dx$$

[brazen frigate]

Rion

[prisma summit]

so you have three integrals to compute with the definition

start with the last one, it is pretty obvious

then, the middle one

after that, check that the quantity you get is indeed equal to what you'd have if you used the antiderivative

finally, the first one: same thing, but that one is mildly harder

[tawny scaffold]

i got the same result tho, 19.5

[prisma summit]

Huh

,w int 4x^2 + x + 1 from -1 to 2

[brazen frigate]

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[tawny scaffold]

its 2 not 1

[prisma summit]

oops mb

,w int 4x^2 + x + 2 from -1 to 2

[brazen frigate]

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Requested by rion___

[prisma summit]

hm ok

[tawny scaffold]

ig the definition part is wrong then

[prisma summit]

well as said, start with the simplest

$2 \int_{-1}^{2} 1 dx$

[brazen frigate]

Rion

[prisma summit]

if you take the sum limit to compute the integral

what do you get?

you should get precisely 3

but I see you didn't get 3 but 15/2

[tawny scaffold]

wait what

[prisma summit]

never mind

my bad

I didn't understand you did some manipulations inside the sum

but don't do that

just compute each integral separately, it will be easier to do a sanity check later

[tawny scaffold]

i basically gave my sanity away when i entered engineering so no worries

[prisma summit]

not the point

[tawny scaffold]

but anyway

[prisma summit]

we just need a means to verify your results as we progress

not just at the end

[tawny scaffold]

but i dont get it u want me not to multiply in the sum? why?

[prisma summit]

As said before

I want you to compute three integrals with the definition

[tawny scaffold]

oh k one min

[prisma summit]

$\int_{-1}^{2} x^2 dx$, $\int_{-1}^{2} x dx$ and $\int_{-1}^{2} 1 dx$

[brazen frigate]

Rion

[prisma summit]

because once you compute these three guys with the sum, we can just multiply and add the results

and it's also easier to do sanity checks in the middle

[tawny scaffold]

got the exact same answer

after multipling its gonna be 19.5 again

[prisma summit]

Hmm

[prisma summit]

ok for the integral of 1dx

ok for the integral of xdx as well

[tawny scaffold]

what about them?

[prisma summit]

I'm just doing individual checks

to make sure they're correct

[tawny scaffold]

oh alr

[prisma summit]

since they're relatively easy to check

(just compute the integral with the antiderivative)

[tawny scaffold]

ic thats why its better to do each bit separately

[prisma summit]

ok for the integral of x²dx too

so yeah, multiply and add

and you got the right result

[prisma summit]

yeah, it's only for the purpose of checking you didn't make mistakes on the way

and if you did, we can find out where you made those mistakes

[tawny scaffold]

well getting the correct answer as the intgreal after doing them individually means did smth wrong in the beginning

[prisma summit]

but you did everything right in your second attempt

[prisma summit]

in this attempt, you got everything right

[tawny scaffold]

yea ig it was just some miscalculation but my first attempt is so congloted i don't want to find it

ig i learned to separate each integral and do the antidrivative on it

[prisma summit]

It is much easier to check that way

[tawny scaffold]

yea thx

+close

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