MATH 100 Solutions – Fundamental Theorem of Calculus & Indefinite Integrals Study Guide PDF

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MATH 100 – November 29 & December 02


University of Alberta


Fall 2024
The Fundamental Theorem of Calculus
Indefinite Integrals




1 (uAlberta) MATH 100 Fall 2024

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The Fundamental Theorem of
Calculus (FTC)




2 (uAlberta) MATH 100 Fall 2024

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Let f be a continuous function on the interval [a, b]. Let x ∈ [a, b] and
consider the integral
! x
g (x) = f (t) dt
a

Geometrically, if f ≥ 0, g (x) gives the area below the graph of f from a to
x.
y




a x b x



3 (uAlberta) MATH 100 Fall 2024

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The Fundamental Theorem of Calculus, Part I
Let f be a function continuous on [a, b]. The function g defined by
! x
g (x) = f (t) dt, x ∈ [a, b],
a

is continuous on [a, b] and differentiable on (a, b) and

g → (x) = f (x).




4 (uAlberta) MATH 100 Fall 2024