approximating area under a curve 58 videos

Using Sine to Calculate the Area of a Triangle
Trigonometry Basic Trigonometry
How to calculate the area of any triangle using two sides and an included angle.
area of a triangle sine 
Using Sine to Calculate the Area of a Triangle
Precalculus Basic Trigonometry
How to calculate the area of any triangle using two sides and an included angle.
area of a triangle sine 
Area of Regular Polygons
Geometry Area
How to derive the formula to calculate the area of a regular polygon.
area apothem side hexagon isosceles triangle perimeter equilateral equiangular 
Area of Trapezoids
Geometry Area
How to derive the area of a trapezoid formula using the area of a rectangle.
trapezoid parallelogram base height 
Area of Kites and Rhombuses
Geometry Area
How to derive the area formula of a kite based on the rectangle formula; how to calculate the area of a rectangle using diagonal lengths.
kite area diagonals consecutive sides vertex angle non vertex angle bisect perpendicular rhombus 
Average Value of a Function
Calculus The Definite Integral
How to find the average value of a function over an interval [a,b].
average value antidifferentiation limits of integration functions area under a curve 
Area and Perimeter of Circles
PreAlgebra Introductory Geometry
Vocabulary and formulas for the area of a circle

Area With the Cross Product
Precalculus Systems of Linear Equations and Matrices
How to show that the magnitude of the cross product of two vectors gives the area of the parallelogram determined by those two vectors.
cross product magnitude of vectors dot product angle between vectors area parallelogram 
Area and Perimeter of Rectangles
PreAlgebra Introductory Geometry
Overview of area and perimeter formulas for parallelograms and rectangles

Volume and Surface Area
PreAlgebra Introductory Geometry
Vocabulary and formulas for surface area and volume of common solids

Families of Polar Curves: Conic Sections
Precalculus Polar Coordinates and Complex Numbers
How to describe the polar equations of conic sections.
polar graph polar equation polar curve conic sections focus origin pole parabola symmetric about the x axis parabola vertex 
Area and Perimeter of Triangles
PreAlgebra Introductory Geometry
Understanding why the area of a triangle is 1/2 base times height

Families of Polar Curves: Circles, Cardiods, and Limacon
Precalculus Polar Coordinates and Complex Numbers
How to graph the special cases of the family r = a + b cos (theta) when a or b = 0.
polar graph polar equation polar curve circles center radius completing the square 
Solving Formulas
Geometry Area
How to strategize about solving formulas for variables; how to solve the area of a rectangle formula for base and height; how to solve the area of a triangle formula for base and for height.
formulas isolating a variable rectangle area triangle area trapezoid area regular polygon area 
Curve Sketching with Derivatives
Calculus Applications of the Derivative
How to evaluate the limit of a function using continuity.

Pythagorean Theorem Proofs
Geometry Pythagorean Theorem
How to prove the Pythagorean Theorem using Algebra to show the area of the smaller square plus the area of four triangles is equal to the area of the larger square.
right triangle area of a square binomial squared area of a triangle side leg hypotenuse 
Pythagorean Theorem Proofs
Trigonometry Pythagorean Theorem
How to prove the Pythagorean Theorem using Algebra to show the area of the smaller square plus the area of four triangles is equal to the area of the larger square.
right triangle area of a square binomial squared area of a triangle side leg hypotenuse 
Similarity and Volume Ratios
Geometry Similarity
How to identify if two solids are similar and how to convert 1D ratios to surface area and volume ratios.
similarity volume ratios surface area 
An Important Limit
Calculus The Derivative
How to interpret the value of a limit important in the derivative of exponential functions.
limits natural logarithm numerical approximation