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▾
Calculus 2
▾
Integration techniques
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Intro to calc 2
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Basic indefinite integrals
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Reverse power rule for indefinite integrals
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Sum, difference, and reverse power rules for indefinite integrals
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Integration by parts
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Integrals involving trig functions
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Lesson
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Practice
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Trig substitutions
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Integration by partial fractions
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Integral recurrence relations
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Integrating quadratics by completing the square
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Integration by long division
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Improper integrals
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Comparison tests for convergence
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Approximating definite integrals
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Riemann sums
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Simpson's rule
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Practice: Simpson's rule
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Trapezoidal rule
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Lesson
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Practice
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Midpoint rule
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Applications of integrals
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Arc length (calculus 2)
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Using the formula
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Center of mass (calculus 2)
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Center of mass for one and two-dimensional systems
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Center of mass for planar lamina
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Pappus's theorem
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Hydrostatic force
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Mode of a continuous random variable from a probability density function
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Surface area of solids of revolution
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Gabriel's Horn
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Applications of trigonometric integrals
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Integrating exponential functions
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Logarithmic functions
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Parametric equations and polar coordinates
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Cycloid area and length
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Eliminating the parameter
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Testing polar equations for symmetry
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Deriving the equations of a cycloid, epicycloid, and hypocycloid
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Series and sequences
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Maclaurin series
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Finding the sum of a telescoping series
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Convergent and divergent geometric series
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Lesson
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Practice
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Alternating harmonic series
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Alternating series test
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Partial sums
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Ratio test
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Root test
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Lesson
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Practice
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Absolute convergence, conditional convergence, and divergence
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Riemann's rearrangement theorem
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Taylor series
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Vectors
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Intro to vectors
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Length of a vector
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Cross product
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Intro to the dot product
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Competition problems (calculus 2)
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Calculus 2
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Integration techniques
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Approximating definite integrals
Midpoint rule
In this section, you will learn how to use the midpoint rule to approximate definite integrals.
YouTube videos
137856
Ex 1: Numerical Integration - The Midpoint Rule
Mathispower4u
137857
Midpoint Rule & Riemann Sums
The Organic Chemistry Tutor
Khan Academy videos
22
Midpoint sums
Khan Academy
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YouTube