Riemann Sum
2 hr 55 min 9 Examples
- Antidifferentiation and integration overview
- Approximating area under a curve
- Riemann Sum, Midpoint, and Trapezoidal Approximation Overview
- Riemann sum and trapezoidal approximation for tables (Examples 1-2)
- Approximations using equal subintervals (Examples 3-4)
- Trapezoidal approximation for a table with unequal widths (Example 5)
- Distance estimation using a velocity graph (Example 6)
- Distance estimates using velocity tables (Examples 7-8)
- Riemann sums and derivative estimation for twice-differentiable functions (Example 9)
Sigma Notation
1 hr 28 min 9 Examples
- What is sigma notation? Evaluate the Sum (Examples #1-3)
- What is the Definition of the Definite Integral?
- Use the definition of the definite integral to rewrite as a limit of finite sums (Examples #4-5)
- Five Summation Formulas
- Use the definition of the definite integral to evaluate (Example #6-7)
- Evaluate the definite integral as a limit of finite sums (Example #8-9)
Integration Rules
1 hr 44 min 19 Examples
- Basic Integration Rules and Formulas
- Antidifferentiate the function (Examples #1-3)
- Evaluate the indefinite integral (Examples #4-7)
- Simplify then find the antiderivative (Examples #8-11)
- Evaluate the integral by simplifying the integrand first (Examples #12-14)
- Evaluate the definite integral using integration formulas (Examples #15-17)
- Discover integration properties for definite integrals (Examples #18-19)
Integral of Exponential Function
55 min 13 Examples
- Introduction to Video: Exponential Integration
- Overview of Integration Rules for Exponential Functions and Logarithmic Functions
- Antidifferentiate the exponential function (Examples #1-2)
- Evaluate the indefinite and definite integral for exponential functions (Examples #3-6)
- Simplify then evaluate using formulas for exponential and logarithmic functions (Examples #7-10)
- Evaluate the integral and use logarithmic properties to simplify (Examples #11-13)
Trig Integrals
55 min 12 Examples
- Introduction to Video: Trig Integrals
- Overview of Rules and Formulas for Integrating Trigonometric Functions
- Antidifferentiate the trig function (Examples #1-3)
- Evaluate the integral using trig identities and formulas (Examples #4-7)
- Evaluate the indefinite integral (Examples 8-9)
- Find the definite integral for the trig function (Example #10)
- Evaluate the definite integral involving trig functions (Examples #11-12)
Inverse Trig Integrals
1 hr 13 Examples
- Introduction to Video: Inverse Trig Integrals
- Overview of formulas for Integrals of Inverse Trig Functions and Half-Angles
- Evaluate the integral of the given arcfunction (Examples #1-2)
- Evaluate the integral for the arcsine and arctangent functions (Examples #3-6)
- Evaluate the integral for the arcsecant and arcsine functions (Example #7-10)
- Evaluate the integral by using half-angle identities (Examples #11-13)
Fundamental Theorem of Calculus
1 hr 24 min 15 Examples
- Review of Integration Rules and Properties
- Evaluate using Integration Properties (Examples #1-3)
- Find area under curve from graph, absolute value integral (Examples #4-5)
- Overview of FTC#1 and evaluate (Examples #6-9)
- Overview of FTC#2 and find F'(x) or F'(a) (Examples #10-15)
U Substitution
1 hr 59 min 15 Examples
- Introduction to Video: U-Substitution
- Overview of integration by substitution (Examples #1-2)
- Evaluate integrals using u-substitution (Examples #3-6)
- Antidifferentiate with double substitution (Example #7)
- Evaluate definite integrals using u-substitution (Examples #8-14)
- Derive formula for tan(ax) using u-sub (Example #15)
Mean Value Theorem for Integrals
1 hr 15 min 10 Examples
- Overview of the Mean Value Theorem for Integrals and Average Value Formula
- Average value of quadratic, general, and trigonometric functions (Examples #1-6)
- Determine values of c satisfying MVT for integrals (Examples #7-9)
- Average temperature and value of c for MVT (Example #10)
Particle Motion
2 hr 17 min 13 Examples
- Overview of acceleration, velocity, position, distance, and displacement
- Definite integrals with initial conditions (Examples #1-4)
- Velocity and position functions from acceleration (Example #5)
- Position of particle from v(t) and object travel distance (Examples #6-7)
- Particle position from acceleration (Example #8)
- Net distance, displacement, and total distance (Example #9)
- v(t) graph analysis: displacement, distance, position (Example #10a-f)
- v(t)=cos(t): change in direction, distance, displacement, position (Example #11a-d)
- Acceleration, motion, position, average velocity from v(t) (Example #12a-d)
- Average acceleration, position, displacement, total distance from v(t) (Example #13a-d)
Simpson’s Rule
2 hr 14 min 10 Examples
- Overview of Midpoint, Trapezoidal, Simpson’s Rule Formulas and Error Bound Formulas
- Approximate integral and find max possible error using Midpoint and Trapezoidal rules (Example #1)
- Estimate max possible error with midpoint and trapezoidal error formulas (Examples #2-3)
- Approximate definite integral and estimate error using Simpson’s rule (Examples #4-6)
- Determine ‘n’ for specified error in Simpson’s rule approximation (Examples #7-8)
- Average value from table using Simpson’s 1/3 rule (Example #9)
- Compare Left/Right Riemann sum, Midpoint, Trapezoidal, and Simpson’s rule approximations (Example #10)
Partial Fraction Decomposition
3 hr 6 min 9 Examples
- Checklist for Integration Techniques with examples
- Partial Fractions steps and rules
- Evaluate using partial fractions – linear distinct/repeating terms (Examples #1-3)
- Evaluate using partial fractions – nonlinear terms, long division (Examples #4-5)
- Integrate using partial fractions – nonlinear repeating terms, synthetic division (Examples #6-7)
- Evaluate definite integral with factoring, grouping, partial fractions (Example #8)
- Integrate using partial fractions, u-sub, completing the square (Example #9)
Integration by Parts
1 hr 31 min 10 Examples
- Overview of Integration by Parts
- Evaluate using integration by parts (Examples #1-3)
- Definite integral with integration by parts (Examples #4-5)
- Double integration by parts (Examples #6-7)
- Integration by parts and u-substitution (Example #8)
- Tabular Method and power of secant integration (Examples #9-10)
Advanced Trigonometric Integration
1 hr 34 min 11 Examples
- Review of Trig Integral Formulas and Identities
- Overview of Rules for Integrals involving Powers of Trigonometric Functions
- Integrate odd sine/even cosine, even sine/odd cosine (Examples #1-2)
- Integrate odd sine/cosine, even sine/cosine (Examples #3-4)
- Evaluate odd tangent/secant, even tangent/secant (Examples #5-6)
- Evaluate even tangent, odd secant with integration by parts (Example #7)
- Definite integral of tangent-cubed (Example #8)
- Overview of Integral Formulas for Sine-Cosine Products with Different Angles
- Evaluate integrals using product-sum identities (Examples #9-11)
Trig Substitution
1 hr 29 min 5 Examples
- Introduction to Video: Trigonometric Substitution for Integrals
- Overview of Trigonometric Substitution for Integrals and Properties
- Evaluate using a trig substitution of sine (Example #1)
- Evaluate using a trig substitution of tangent for the indefinite and definite integral (Examples #2a,b)
- Integrate using a trig substitution of secant (Example #3)
- Antidifferentiate using a tangent substitution (Example #4)
- Evaluate by using the trigonometric substitution of sine and u-substitution (Example #5)
Improper Integrals
2 hr 11 min 13 Examples
- Improper Integration Rules
- Evaluate integrals with one infinite limit (Examples #1-4)
- Evaluate improper integrals using integration by parts (Examples #5-6)
- Integrate with both limits of integration infinite (Examples #7-8)
- Evaluate improper integrals with discontinuities (Examples #9-12)
- Evaluate improper integral using advanced trig substitution (Example #13)
Chapter Test
4 hr 10 min 37 Examples
- 37 Challenging Practice Problems
- Great for checking your knowledge
- Perfect for preparing for an in-class assessment
