menu_open Limit of Sequences Limit of a Sequence - Convergence, Divergence Limit of a Sequence -Properties, Calculating, Ordering Convergence and Divergence of Geometric Sequences Series - Definition, Properties, Convergence, Divergence Geometric Series - Definition, Convergence and Divergence Applications of Geometric Series - Geometry, Repeating Decimals Differentiation Differentiation of Various Functions Limits of Exponential and Logarithmic Functions Differentiation of Exponential and Logarithmic Functions Addition Formulas for Trigonometric Functions Limits of Trigonometric Functions Derivatives of Trigonometric Functions Various Methods of Differentiation Quotient Rule for Differentiation Chain Rule for Differentiation Differentiation of Parametric Equations Differentiation of Implicit and Inverse Functions Second Derivative Application of Derivatives Equation of the Tangent Line Increase and Decrease of Functions Solving Equations and Inequalities Velocity and Acceleration Integration Various Methods of Integration Integration of Various Functions Integration by Parts Substitution Method of Integration Application of Definite Integrals Definite Integrals and Series Area Volume Velocity and Distance
Relationship Between Definite Integrals and Series Sums
When a function
is continuous on the closed interval
:
where
and
.
into
subintervals and summing the areas of the corresponding rectangles.The following methods express series as definite integrals :
