Calculus
Integration and accumulation of change
- Exploring accumulations of change
- Approximating areas with Riemann sums
- Riemann sums, summation notation, and definite integral notation
- The fundamental theorem of calculus and accumulation functions
- Interpreting the behavior of accumulation functions involving area
- Applying properties of definite integrals
- The fundamental theorem of calculus and definite integrals
- Finding antiderivatives and indefinite integrals: basic rules and notation: reverse power rule
- Finding antiderivatives and indefinite integrals: basic rules and notation: common indefinite integrals
- Finding antiderivatives and indefinite integrals: basic rules and notation: definite integrals
- Integrating using substitution
- Integrating functions using long division and completing the square
- Using integration by parts
- Integrating using linear partial fractions
- Evaluating improper integrals
Register for a session to review this topic with a small group of learners.
Ic
Calculus · series session
Integration and accumulation of change
We will introduce integrals, understand what they mean, and learn simple integration techniques/rules.
BL
BC
Bill C
0
14/20
Ic
Calculus · series session
Integration and accumulation of change
We will learn more integration techniques (u substitution) and find area and volume using integration.
BL
BC
Bill C
0
14/20
Ic
Calculus · session
Integration: Notation and Techniques
Hi! My name is Advait and I'm here to teach you all about integrals! This will cover the proper integral notation and many integration techniques! I got a 5 on AP Calculus BC, so I hope to share my wealth of knowledge with you all.
Please only join this session if you feel comfortable with derivatives and limits as we will not have time to go over them during the session. However, if you have any calculus-related questions, you can also ask me after the session.
Hopefully we will be able to finish everything, but if not, I plan to do a part 2 to this session later on!
BL
AS
Advait S
0
1/50
Ic
Calculus · series session
Integration and accumulation of change
Integration: Riemann sums, integral notation, and some properties!
SL
LG
Luca G
0
12/200
Ic
Calculus · series session
Integration and accumulation of change
- Accumulations of change
- Definition of the integral
- Definite and indefinite integrals
- Definite integrals as "area under the curve"
- Riemann sums
- Average value of a function
- Fundamental Theorem of Calculus
- Reverse power rule
- Common indefinite integrals to memorize
- Using u-substitution to integrate a function
(NOTE: Volumes of solids are not covered in our discussion of integrals.)
SL
PM
Piyush M
0
2/15
Ic
Calculus · series session
Integration and accumulation of change
6.1 - What do integrals mean in context?
6.2 - How can we approximate areas using different types of Riemann sums?
6.3 - How do we convert summation notation expressions into definite integrals?
BL
WB
William B
0
7/50
Ic
Calculus · series session
Integration and accumulation of change
6.4 - What is the FTC?
6.5 - How can we predict the behavior of an antiderivative from an equation?
6.6 - What happens if we do the following to an integral:
Switch the bounds?
Add a coefficient inside the integral?
Add multiple expressions?
6.7 - How can we evaluate the derivative of an integral with variable bounds?
6.8 - What is an indefinite integral?
6.9 - How can we solve integrals using u-substitution?
6.10 - How can we solve integrals using long division or completing the square?
BL
WB
William B
0
7/50
Ic
Calculus · series session
Integration and accumulation of change
(BC only) 6.11 - How can we solve integrals by reversing product rule?
(BC only) 6.12 - How can we solve integrals by decomposing a function into linear partial fractions?
(BC only) 6.13 - How can we evaluate integrals with improper bounds?
BL
WB
William B
0
7/50
That's it for now!
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