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2.2 Integral Calculus
Take the next step on the calculus journey with integrals and sums.
Calculating Distance
Using Riemann Sums
The Definite Integral
First Calculations
The Fundamental Theorem of Calculus
Integrating Polynomials
Substitution
Exponentials and Trig
Integration by Parts
Basics of Partial Fractions
Trigonometric Integrals
Trig Substitution
Integration in the World
Area and Probability
Calculating Volume
Arc Length and Surface Area
Integration in Physics I
Application: Differential Equations
Integration in Physics II
Zeno's Paradox & Sums
Sums and Sigma Notation
Secret Identities
Converging Sums
Ratio and Root Tests
The Integral Test
Rearrangements: 0=1?
Limit Comparison Test
Power Series
Basics of Fourier Series
Course description
In a sense, differential calculus is local: it focuses on aspects of a function near a given point, like its rate of change there. Integral calculus complements this by taking a more complete view of a function throughout part or all of its domain. This course provides complete coverage of the two essential pillars of integral calculus: integrals and infinite series. By the end, you'll know their core principles and how to apply them to problems in geometry, probability, and physics.
Topics covered
- Applications of infinite sums
- Applications of integrals
- Convergence tests
- Integration by parts
- Partial fractions
- Polynomial integrals
- Power series
- Riemann sums
- Substitution rule
- The Fundamental Theorem
- Transcendental integrals
- Trigonometric integrals
Prerequisites and next steps
You’ll need an understanding of algebra and the basics of functions, such as domain and range, graphs, and intercepts. You should also be familiar with exponential functions, logarithms, and basic trigonometric identities. A strong understanding of differential calculus is a must.
Up next
3.1 Multivariable Functions
Discover the multi-dimensional space of multivariable functions, and learn how to think about scenarios with more than one changing parameter.
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