www.stuvia.com/doc/2026//2027.100%A+
MATH 100 – November 29 & December 02
University of Alberta
Fall 2024
The Fundamental Theorem of Calculus
Indefinite Integrals
1 (uAlberta) MATH 100 Fall 2024
, www.stuvia.com/doc/2026//2027.100%A+
The Fundamental Theorem of
Calculus (FTC)
2 (uAlberta) MATH 100 Fall 2024
, www.stuvia.com/doc/2026//2027.100%A+
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
, www.stuvia.com/doc/2026//2027.100%A+
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
MATH 100 – November 29 & December 02
University of Alberta
Fall 2024
The Fundamental Theorem of Calculus
Indefinite Integrals
1 (uAlberta) MATH 100 Fall 2024
, www.stuvia.com/doc/2026//2027.100%A+
The Fundamental Theorem of
Calculus (FTC)
2 (uAlberta) MATH 100 Fall 2024
, www.stuvia.com/doc/2026//2027.100%A+
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
, www.stuvia.com/doc/2026//2027.100%A+
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
