Fundamental Theorems of Calculus

The first fundamental theorem of calculus states that, if is Continuous on theClosed Interval and is the Antiderivative (Indefinite Integral) of on , then

(1)

The second fundamental theorem of calculus lets be Continuous on an Open Interval and lets be any point in . If is defined by

(2)

(3)

The complex fundamental theorem of calculus states that if has a ContinuousAntiderivative in a region containing a parameterized curve for , then

(4)

• Substitution Map
• Subtend
• Subtraction
• Succeeds
• Successes
• Sufficient
• Suitable Number
• Sum
• Summand
• Summatory Function
• Sum-Product Number
• Sum Rule
• Sup
• Characteristic (Partial Differential Equation)
• Characteristic Polynomial
• Characteristic (Real Number)
• Character (Multiplicative)
• Character (Number Theory)
• Character Table
• Charlier's Check
• Chasles-Cayley-Brill Formula
• Chasles's Contact Theorem
• Chasles's Polars Theorem
• Chasles's Theorem
• Chebyshev Approximation Formula