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▾
Calculus 2
▾
Integration techniques
•
Intro to calc 2
▸
Basic indefinite integrals
•
Reverse power rule for indefinite integrals
•
Sum, difference, and reverse power rules for indefinite integrals
•
Integration by parts
▸
Integrals involving trig functions
•
Lesson
•
Practice
•
Trig substitutions
•
Integration by partial fractions
•
Integral recurrence relations
•
Integrating quadratics by completing the square
•
Integration by long division
•
Improper integrals
•
Comparison tests for convergence
▾
Approximating definite integrals
•
Riemann sums
▸
Simpson's rule
•
Practice: Simpson's rule
▸
Trapezoidal rule
•
Lesson
•
Practice
•
Midpoint rule
▸
Applications of integrals
▸
Arc length (calculus 2)
•
Using the formula
▸
Center of mass (calculus 2)
•
Center of mass for one and two-dimensional systems
•
Center of mass for planar lamina
•
Pappus's theorem
•
Hydrostatic force
•
Mode of a continuous random variable from a probability density function
•
Surface area of solids of revolution
•
Gabriel's Horn
•
Applications of trigonometric integrals
•
Integrating exponential functions
•
Logarithmic functions
▸
Parametric equations and polar coordinates
•
Cycloid area and length
•
Eliminating the parameter
•
Testing polar equations for symmetry
•
Deriving the equations of a cycloid, epicycloid, and hypocycloid
▸
Series and sequences
•
Maclaurin series
•
Finding the sum of a telescoping series
▸
Convergent and divergent geometric series
•
Lesson
•
Practice
•
Alternating harmonic series
•
Alternating series test
•
Partial sums
•
Ratio test
▸
Root test
•
Lesson
•
Practice
•
Absolute convergence, conditional convergence, and divergence
•
Riemann's rearrangement theorem
•
Taylor series
▸
Vectors
•
Intro to vectors
•
Length of a vector
•
Cross product
•
Intro to the dot product
•
Competition problems (calculus 2)
›
Calculus 2
›
Integration techniques
›
Approximating definite integrals
Riemann sums
This is a skill. Make "Lesson" and "Practice" sections.
YouTube videos
2753
4.2 Intro to Area Under a Curve
rootmath
2758
4.2 Estimating the Area Under a Curve
rootmath
3242
Riemann Sums - Midpoint, Left & Right Endpoints, Area, Definite Integral, Sigma Notation, Calculus
The Organic Chemistry Tutor
3243
Riemann Sums - Left Endpoints and Right Endpoints
The Organic Chemistry Tutor
3244
❖ Calculating a Definite Integral Using Riemann Sums - Part 1 ❖
patrickJMT
3245
Calculating a Definite Integral Using Riemann Sums - Part 2
patrickJMT
4326
A Brief Introduction to a Riemann Sum
Cole's World of Mathematics
4346
AP Calculus AB: A Riemann Sum from a Table of Values
Cole's World of Mathematics
14123
Applying iram to a table of values
Brian McLogan
13751
Applying reimann sum for the midpoint rule and 3 partitions
Brian McLogan
More YouTube videos...
Khan Academy videos
18
Riemann approximation introduction
Khan Academy
~
YouTube
19
Over- and under-estimation of Riemann sums
Khan Academy
~
YouTube
20
Worked example: finding a Riemann sum using a table
Khan Academy
~
YouTube
21
Worked example: over- and under-estimation of Riemann sums
Khan Academy
~
YouTube
Khan Academy exercises
Left & right Riemann sums
Khan Academy
Over- and under-estimation of Riemann sums
Khan Academy