**KHAN ACADEMY VIDEOS**

CHAPTER 4

CHAPTER 4

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**Khan Academy****CHAPTER 4:**

INTEGRATION

INTEGRATION

__Left & right Riemann sums__

Riemann approximation introduction

Over- and under-estimation of Riemann sums

Worked example: finding a Riemann sum using a table

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

Midpoint sumsRiemann approximation introduction

Over- and under-estimation of Riemann sums

Worked example: finding a Riemann sum using a table

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

Midpoint sums

**Trapezoidal sums**

**Summation notation**

Worked examples: Summation notationWorked examples: Summation notation

**Riemann sums in summation notation**

Worked example: Riemann sums in summation notationWorked example: Riemann sums in summation notation

**Worked example: Rewriting definite integral as limit of Riemann sum**

Worked example: Rewriting limit of Riemann sum as definite integralWorked example: Rewriting limit of Riemann sum as definite integral

**Antiderivatives and indefinite integrals**

Fundamental theorem of calculus (Part 1)

Fundamental theorem of calculus (Part 2)

Worked example: Finding derivative with fundamental theorem of calculus

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

Finding derivative with fundamental theorem of calculus: x is on both boundsFundamental theorem of calculus (Part 1)

Fundamental theorem of calculus (Part 2)

Worked example: Finding derivative with fundamental theorem of calculus

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

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

**Reverse power rule**

Indefinite integrals: sums & multiples

Rewriting before integratingIndefinite integrals: sums & multiples

Rewriting before integrating

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

**Breaking up integral interval**

Definite integral over a single point

Switching bounds of definite integral

Worked examples: Definite integral properties 1

Integrating sums of functions

Integrating scaled version of function

Worked examples: Definite integral properties 2

Definite integral properties (no graph): function combination

Definite integral properties (no graph): breaking intervalDefinite integral over a single point

Switching bounds of definite integral

Worked examples: Definite integral properties 1

Integrating sums of functions

Integrating scaled version of function

Worked examples: Definite integral properties 2

Definite integral properties (no graph): function combination

Definite integral properties (no graph): breaking interval

**Functions defined by integrals**

Functions defined by integrals: switched intervalFunctions defined by integrals: switched interval

**Definite integrals: reverse power rule**

Definite integral of rational function

Definite integral of radical function

Definite integral of trig function

Definite integral involving natural log

Definite integral of piecewise function

Definite integral of absolute value functionDefinite integral of rational function

Definite integral of radical function

Definite integral of trig function

Definite integral involving natural log

Definite integral of piecewise function

Definite integral of absolute value function

**𝘶-substitution intro**

𝘶-substitution: multiplying by a constant

𝘶-substitution: defining 𝘶

𝘶-substitution: defining 𝘶 (more examples)

𝘶-substitution: rational function

𝘶-substitution: logarithmic function

𝘶-substitution: definite integrals

𝘶-substitution: challenging definite integral𝘶-substitution: multiplying by a constant

𝘶-substitution: defining 𝘶

𝘶-substitution: defining 𝘶 (more examples)

𝘶-substitution: rational function

𝘶-substitution: logarithmic function

𝘶-substitution: definite integrals

𝘶-substitution: challenging definite integral

__Average value over a closed interval__

Calculating average value of function over interval

Mean value theorem for integralsCalculating average value of function over interval

Mean value theorem for integrals

**Interpreting behavior of 𝑔 from graph of 𝑔'=ƒ**

Visually determining antiderivativeVisually determining antiderivative