Integrals videos

Introduction to integral calculus

Definite integrals intro

Worked example: accumulation of change

Riemann approximation introduction

Over- and under-estimation of Riemann sums

Worked example: finding a Riemann sum using a table

Midpoint sums

Worked example: over- and under-estimation of Riemann sums

Trapezoidal sums

Motion problem with Riemann sum approximation

Summation notation

Worked examples: Summation notation

Riemann sums in summation notation

Worked example: Riemann sums in summation notation

Midpoint and trapezoidal sums in summation notation

Riemann sums in summation notation: challenge problem

Definite integral as the limit of a Riemann sum

Worked example: Rewriting definite integral as limit of Riemann sum

Worked example: Rewriting limit of Riemann sum as definite integral

The fundamental theorem of calculus and accumulation functions

Functions defined by definite integrals (accumulation functions)

Finding derivative with fundamental theorem of calculus

Finding derivative with fundamental theorem of calculus: chain rule

Interpreting the behavior of accumulation functions

Negative definite integrals

Finding definite integrals using area formulas

Definite integral over a single point

Integrating scaled version of function

Switching bounds of definite integral

Integrating sums of functions

Definite integrals on adjacent intervals

Worked examples: Finding definite integrals using algebraic properties

Worked example: Breaking up the integral's interval

Finding derivative with fundamental theorem of calculus: x is on lower bound

Functions defined by integrals: switched interval

Worked example: Merging definite integrals over adjacent intervals

Finding derivative with fundamental theorem of calculus: x is on both bounds

Functions defined by integrals: challenge problem

Antiderivatives and indefinite integrals

The fundamental theorem of calculus and definite integrals

Reverse power rule

Indefinite integrals: sums & multiples

Rewriting before integrating

Rewriting before integrating: challenge problem

Indefinite integrals of sin(x), cos(x), and eˣ

Indefinite integral of 1/x

Definite integral of rational function

Definite integrals: reverse power rule

Definite integral of radical function

Definite integral of trig function

Definite integral of piecewise function

Definite integral of absolute value function

Definite integral involving natural log

𝘶-substitution intro

𝘶-substitution: multiplying by a constant

𝘶-substitution: defining 𝘶 (more examples)

𝘶-substitution: defining 𝘶

𝘶-substitution: logarithmic function

𝘶-substitution: definite integrals

𝘶-substitution: rational function

𝘶-substitution: definite integral of exponential function

𝘶-substitution: special application

𝘶-substitution: double substitution

𝘶-substitution: challenging application

Integration using long division

Integration using completing the square and the derivative of arctan(x)

Integral of sin^2(x) cos^3(x)

Integral of cos^3(x)

Integral of sin^4(x)

Proof of fundamental theorem of calculus

Intuition for second part of fundamental theorem of calculus