Fundamental Theorem of Calculus Courses and Certifications

Khan Academy

Intuition for Second Part of Fundamental Theorem of Calculus - AP Calculus AB - Khan Academy

Build intuition for the second part of the Fundamental Theorem of Calculus by connecting area under a curve with antiderivatives and definite integrals.

• YouTube
• 12 minutes
• Self-Paced
• Free Video

Professor Leonard

Calculus 1 - The Fundamental Theorem of Calculus

An introductory lecture on the Fundamental Theorem of Calculus in a first-course calculus sequence.

• YouTube
• 2 hours 46 minutes
• Self-Paced
• Free Video

Michael Penn

Real Analysis - The Fundamental Theorem of Calculus

A concise proof of both parts of the Fundamental Theorem of Calculus from a real analysis perspective.

• YouTube
• 23 minutes
• Self-Paced
• Free Video

University of Huddersfield

Integral Calculus & The Fundamental Theorem

Calculate definite and indefinite integrals using partial fractions and integration by parts, apply them to areas, volumes of revolution and arc length, and prove the fundamental theorem.

• Coursera
• 3 weeks, 4 hours a week
• Self-Paced
• Paid Course

3Blue1Brown

Integration and the Fundamental Theorem of Calculus

An intuitive, visual explanation of why integrals measure signed area and reverse differentiation, using a moving car’s velocity to motivate the fundamental theorem of calculus.

• YouTube
• 21 minutes
• Self-Paced
• Free Video

Cálculo Diferencial e Integral unidos por el Teorema Fundamental del Cálculo

726 ratings at Coursera

Curso que conecta derivada e integral desde el inicio mediante el Teorema Fundamental del Cálculo para predecir magnitudes cambiantes.

• Coursera
• 13 weeks, 3 hours a week
• Self-Paced
• Paid Course

Calculus: Single Variable Part 3 - Integration

552 ratings at Coursera

Integrate differential equations, learn core techniques of integration, apply the Fundamental Theorem of Integral Calculus, and tackle difficult integrals using big-O reasoning.

• Coursera
• 4 weeks, 3 hours a week
• Self-Paced
• Free Online Course

Fundamental Theorem of Calculus - Lecture 19

Explore the essential connection between differentiation and integration through two versions of the fundamental theorem, plus improper integrals and unbounded functions.

• YouTube
• 1 hour 20 minutes
• Self-Paced
• Free Video

Dot Physics

The Fundamental Theorem of Calculus: Integrals as Anti-Derivatives

Explore the fundamental theorem of calculus through position and velocity, with interactive Python code demonstrations for derivatives and integrals.

• YouTube
• 20 minutes
• Self-Paced
• Free Video

Math with Professor V

The Fundamental Theorem of Calculus in Business Mathematics - Lesson 7.4

Master the Fundamental Theorem of Calculus through clear explanations and practical examples of definite integrals, including techniques for u-substitution and working with changing integration limits.

• YouTube
• 51 minutes
• Self-Paced
• Free Video

Algebraic Calculus One

An algebraic approach to integral calculus for curves, using affine geometry, signed area, and discrete calculus.

• OpenLearning
• Self-Paced
• Paid Course

Calculus through Data & Modelling: Series and Integration

63 ratings at Coursera

Learn integration: build definite integrals from Riemann sums, apply the Fundamental Theorem of Calculus, find antiderivatives, and approximate hard integrals with tables and estimation.

• Coursera
• 5 weeks, 2 hours a week
• Self-Paced
• Paid Course

Krista King

Calculus II - Integrals, Applications, Polar and Parametric Equations, Sequences and Series

Master advanced integration techniques, series convergence, and polar coordinates through comprehensive problem-solving in this intensive mathematical journey.

• YouTube
• 1 day 8 hours 9 minutes
• Self-Paced
• Free Video

Krista King

Calculus Integrals - Complete Course on Antiderivatives, Definite Integrals, and Integration Techniques

Master comprehensive integration techniques from basic antiderivatives to advanced methods like partial fractions, trigonometric substitution, and improper integrals.

• YouTube
• 11 hours 2 minutes
• Self-Paced
• Free Video

MathTrackX: Integral Calculus

Discover concepts and techniques relating to integration and how they can be applied to solve real world problems.

• edX
• 4 weeks, 3-6 hours a week
• Self-Paced
• Free Online Course (Audit)