output.to from Sideway

~~Calculus~~

Calculus TOC Calculus Differentiation~~Integration~~

Integral Rules of Integration~~Applications of Integration~~

Interpretation Geometrical~~Physical~~Approximation

~~Summation of Accumulative Physical Quantity~~Average of Accumulative Physical Quantity Anti-derivative of Physical Quantity

~~Area of Plane Shapes~~Volume of Common Solids Mechanical Quantities Probability

`-=[]⟨⟩\;',./~!@#$%^&*()_+{}|:"<>? 𝑎𝑏𝑐𝑑𝑒𝑓𝑔ℎ𝑖𝑗𝑘𝑙𝑚𝑛𝑜𝑝𝑞𝑟𝑠𝑡𝑢𝑣𝑤𝑥𝑦𝑧 Å − × ⋅∓±∘꞊﹦∗∙ ℯ 𝔸𝔹ℂ𝔻𝔼𝔽𝔾ℍ𝕀𝕁𝕂𝕃𝕄ℕ𝕆ℙℚℝ𝕊𝕋𝕌𝕍𝕎𝕏𝕐ℤ𝐴𝐵𝐶𝐷𝐸𝐹𝐺𝐻𝐼𝐽𝐾𝐿𝑀𝑁𝑂𝑃𝑄𝑅𝑆𝑇𝑈𝑉𝑊𝑋𝑌𝑍 ∼∽∾≁≂≃≄≅≆≇≈≉≌≐≠≡ ≤≥≦≧≨≩≪≫ ∈∉∊∋∌∍ ⊂⊃⊄⊅⊆⊇ 𝛼𝛽𝛾𝛿𝜀𝜁𝜂𝜃𝜄𝜅𝜆𝜇𝜈𝜉𝜊𝜋𝜌𝜎𝜏𝜐𝜑𝜒𝜓𝜔 ∀∂∃∅⦰∆∇∎∞∝∴∵ ∏∐∑⋀⋁⋂⋃ ∧∨∩∪ ∫∬∭∮∯∰∱∲∳ ∥⋮⋯⋰⋱ ‖ ′ ″ ‴ ⁄ ⁗ ʹ ʺ ‵ ‶ ‷ ﹁﹂﹃﹄︹︺︻︼ ︗ ︘ ︿﹀︽︾﹇﹈︷︸ ⏜ ⏝ ⎴ ⎵ ⏞ ⏟ ⏠ ⏡ ←↑→↓↤↦↥↧↔↕↖↗↘↙▲▼◀▶↺↻⟲⟳ ↼↽↾↿⇀⇁⇂⇃⇄⇅⇆⇇ ⇐⇑⇒⇓⇔⇌⇍⇏⇕⇖⇗⇘⇙⇙⇳⥢⥣⥤⥥⥦⥧⥨⥩⥪⥫⥬⥭⥮⥯

Draft for Information Only

Content


    Summation of Accumulative Physical Quantity
 
    Areas of plane shapes

Summation of Accumulative Physical Quantity

Areas of plane shapes can be determined by integration when the area of a plane shape is expressed as an infinitesimal area element that can be summed by the application of integration.

Areas of plane shapes

Area of Ellipse

Area of ellipse by area under curve.

By subsitution
Area of Circle

Area of circle is a special case of ellipse. The area of circle can be obtained by letting b=a
Area of Circular Sector

Area of circular sector by horizontal summation approach

Area of triangles

Area under arc

Area of circular sector
Area of circular segment

Area of circular segment by area subtraction

Area of circular segment in terms of height of arced portion, h