EE-Learning
Over- and under-estimation of Riemann sums
Catogry:
Math
Subject:
AP Calculus AB
Course:
Integration And Accumulation Of Change
Lecture List
Intuition for second part of fundamental theorem of calculus
Proof of fundamental theorem of calculus
Integration using completing the square and the derivative of arctan(x)
Integration using long division
𝘶-substitution: definite integral of exponential function
𝘶-substitution: definite integrals
𝘶-substitution: logarithmic function
𝘶-substitution: rational function
𝘶-substitution: defining 𝘶 (more examples)
𝘶-substitution: defining 𝘶
𝘶-substitution: multiplying by a constant
𝘶-substitution intro
Definite integral of absolute value function
Definite integral of piecewise function
Definite integral involving natural log
Definite integral of trig function
Definite integral of radical function
Definite integral of rational function
Definite integrals: reverse power rule
Indefinite integrals of sin(x), cos(x), and eˣ
Indefinite integral of 1/x
Rewriting before integrating
Indefinite integrals: sums & multiples
Reverse power rule
Antiderivatives and indefinite integrals
The fundamental theorem of calculus and definite integrals
Finding derivative with fundamental theorem of calculus: x is on both bounds
Finding derivative with fundamental theorem of calculus: x is on lower bound
Functions defined by integrals: switched interval
Worked example: Merging definite integrals over adjacent intervals
Worked example: Breaking up the integral's interval
Definite integrals on adjacent intervals
Worked examples: Finding definite integrals using algebraic properties
Integrating sums of functions
Switching bounds of definite integral
Integrating scaled version of function
Definite integral over a single point
Finding definite integrals using area formulas
Negative definite integrals
Interpreting the behavior of accumulation functions
Worked example: Finding derivative with fundamental theorem of calculus
Functions defined by definite integrals (accumulation functions)
The fundamental theorem of calculus and accumulation functions
Worked example: Rewriting limit of Riemann sum as definite integral
Worked example: Rewriting definite integral as limit of Riemann sum
Definite integral as the limit of a Riemann sum
Worked example: Riemann sums in summation notation
Riemann sums in summation notation
Worked examples: Summation notation
Summation notation
Trapezoidal sums
Midpoint sums
Worked example: over- and under-estimation of Riemann sums
Worked example: finding a Riemann sum using a table
Over- and under-estimation of Riemann sums
Riemann approximation introduction
Worked example: accumulation of change
Definite integrals intro
Introduction to integral calculus