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/sci/ - Science & Math


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9398990 No.9398990 [Reply] [Original]

>tfw finished calc 1-3 and differential equations
>still don't understand the fundamental theorem of calculus

>> No.9399084

What do you not understand?

>> No.9399088

>>9399084
The fundamental theorem of calculus.

>> No.9399093

>>9399088
What exactly do you not understand about it you faggot?

>> No.9399095
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9399095

>>9398990
ebin

>> No.9399104

>>9398990
you obviously understand it, or otherwise you wouldn't have passed calc 1
it's just that you're so familiar with it that you don't understand why would anyone say that it's such an important theorem
you intuitively know that integration is done by anti-differentiation, well the thing is, that wasn't such an obvious concept in the past, when they realized it, it turned out to completely revolutionize calculus

>> No.9399111

>>9399104
I know how to apply it, but the proof of it still goes over my head. The second part is obvious to me, but what does the first row mean? >>9399095

>> No.9399116

>>9399111
The derivative of the function that is defined as the integral from some fixed point a to the variable x is the integrand evaluated at the point x.

>> No.9399117

>>9399111
I think it means if you take the derivative of the integral you get the same function back

>> No.9399128

Proof is trivial if you know Riemann sums
https://ocw.mit.edu/courses/mathematics/18-01sc-single-variable-calculus-fall-2010/unit-3-the-definite-integral-and-its-applications/part-b-second-fundamental-theorem-areas-volumes/session-52-proving-the-fundamental-theorem-of-calculus/MIT18_01SCF10_Ses52b.pdf

>> No.9399130
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9399130

>>9398990
watch 3blue1brown

>> No.9399133

>>9399128
this is how I was taught it (like with limits and Riemann sums)

>> No.9399147

>>9399128
Isn't this the second theorem?

>> No.9399216

>>9399104
if you believe what you just said, you understand absolutely nothing about maths or physics

t. PhD in algebraic geometry