2. Each branch of mathematics has its own fundamental theorem(s).
If you check out the word fundamental in the dictionary,
you will see that it relates to the foundation
or the base
or is elementary.
Fundamental theorems are important foundations
for the rest of the material to follow.
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13. By definition of indefinite integral
g(x1)g(a) = g'(c1) = f(c1)
Height
c1 c2 c3 cn
Slope Slope of
of = of = Riemann
secant line tangent line rectangle
f(cn)
f(c1) By Mean Value theorem
f(c2)
f(c3)
.............................
n subdivisions
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14. Shazaam!
Math Magic
1. f is an integrable function and
If: 2. g is an antiderivative of f,
b
Then ∫f (x) dx = g(b) g(a)
a
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