| Definition and Properties |
The Geometric Definition of Definite Integrals
The Algebraic Definition of Definite Integrals
Properties of Definite Integrals
| Fundamental Theorems of Calculus |
The First Fundamental Theorem of Calculus
The Second Fundamental Theorem of Calculus
| Techniques of Integration |
Substitution Method
Integration by Parts
| First Fundamental Theorem of Calculus |
| Key Topics Remaining: The Second Fundamental Theorem of Calculus » Substitution Method » Integration by Parts |
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Theorem. If f
(x)
is continuous on (a,b),
then the function Proof. Let us recall the definition of the derivative: By Property 7, Applying Property 8 to the interval [x, x + Δx], we find that where Combining these results, we get Therefore, the function is the set of all primitives of f (x). |
is a primitive of 
.
.
,
.
.
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