Created on: August 6, 2010

Website Address: https://library.curriki.org/oer/Definite-Integrals

TABLE OF CONTENTS

- Limits
- Derivatives
- The Chain Rule
- Derivatives of Special Functions
- Implicit Differentiation
- Minima and Maxima
- Optimization Problems
- Indefinite Integrals
- Definite Integrals
- Solids of Revolution
- Sequences and Series
- Polynomial Approximations
- Partial derivatives
- AP Calculus BC
- Partial Derivatives
- Double Integrals
- Line Integrals I
- Vectors
- Line Integrals II
- Green's Theorem
- L'Hospital's Rule

- Proof: d/dx(x^n)
- Proof: d/dx(sqrt(x))
- Proof: d/dx(ln x) = 1/x
- Proof: d/dx(e^x) = e^x
- Proofs of Derivatives of Ln(x) and e^x
- Calculus: Derivative of x^(x^x)
- Extreme Derivative Word Problem (advanced)

- Position Vector Valued Functions
- Derivative of a position vector valued function
- Differential of a vector valued function
- Vector valued function derivative example
- Line Integrals and Vector Fields

- Introduction to definite integrals
- Definite integrals (part II)
- Definite Integrals (area under a curve) (part III)
- Definite Integrals (part 4)
- Definite Integrals (part 5)
- Definite integral with substitution
- Integrals: Trig Substitution 1
- Integrals: Trig Substitution 2
- Integrals: Trig Substitution 3 (long problem)
- Introduction to differential equations

substitution

This video presents the problem of finding the area under a curve as an anti-derivative problem.

This video continues to solve the same area problem by integration.

This video explores the area under a different curve and solves it using integration.

This video uses the definite integral to compute the areas under a bunch of curves.

This video restates the fundamental theorem of calculus and applies it to various area problems.

This video solves a definite integral involving trig functions by substitution.

This video continues solving trig integrals by substitution.

This video continues looking at trig integrals by substitution.

This more difficult problem involves various substitution techniques.

This video introduces differential equations as an extension to integration.