In this video I go over a useful four-step strategy of integration. This strategy requires understanding and memorization of the basic integration formulas as well as understanding the various integration techniques. In this video I go over ways in selecting the proper integration techniques to use for any given integral and also show how sometimes the most useful method is to simply try random techniques in hopes that the solution will be more recognizable. Also, when stuck in any given integral it is important to try different techniques again as often times multiple techniques or even combination of integration techniques are required for integrating the integral. Download the notes in my video: https://1drv.ms/b/s!As32ynv0LoaIhd0cEFHu_w5Go4MFSw View Video Notes on Steemit: https://steemit.com/mathematics/@mes/strategy-for-integration Related Videos: Integration by Partial Fractions: http://youtu.be/r07NnKf76og Trigonometric Substitution for Integrals: http://youtu.be/2pWvGXwtVJo Integration by Parts: Proof: http://youtu.be/TZhEOct5u_M The Substitution Rule for Integrals: http://youtu.be/VsLC-0g6hVg . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: Official Website: https://MES.fm Steemit: https://steemit.com/@mes Gab: https://gab.ai/matheasysolutions Minds: https://minds.com/matheasysolutions Twitter: https://twitter.com/MathEasySolns Facebook: https://fb.com/MathEasySolutions LinkedIn: https://mes.fm/linkedin Pinterest: https://pinterest.com/MathEasySolns Instagram: https://instagram.com/MathEasySolutions Email me: contact@mes.fm Try our Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Try our Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps ... https://www.youtube.com/watch?v=7JxW2N7izF0

In this video I go over Question 1 of the Laboratory Project: Putting 3D in Perspective and this time determine the points at which a 3D line needs to be clipped before it is projected onto a 2D screen. To do this, I first obtain the equations of the 4 clipping planes which project from the point of view of the camera or eyes and unto the vertices of the projected screen. Then we can plug in the equation of the 3D line into each linear equation of the planes and obtain points at which the line and planes intersect. Graphing this out in the amazing GeoGebra 3D graphing calculator, it becomes clear that the line only needs to be clipped at the left and top clipping planes. This is an important exercise in the mathematics of projecting 3D images onto 2D screens, which are used throughout computer graphics programming. Here is a link to GeoGebra if you want to play around with the projection: https://www.geogebra.org/calculator/twezjbu5 The timestamps of key parts of the video are listed below: - Laboratory Project: Putting 3D in Perspective: 0:00 - Question 1: Clipping a 3D Line: 2:08 - Solution: Graphing out the question in GeoGebra: 2:38 - We need 4 clipping planes: 4:35 - Recap on the equations of lines and planes: 6:58 - Vector and Parametric Equations of the 3D line: 8:17 - Equation of the right clipping plane: 12:21 - Note on simplified vectors: 21:49 - Linear equation of the right clipping plane: 22:49 - Plugging in equation of a line into the equation of a plane: 24:30 - Plotting our right clipping plane in GeoGebra: 30:49 - Equation of the top clipping plane: 32:47 - Plugging in equation of a line into the equation of a plane: 40:46 - Equation of the left clipping plane: 47:13 - Plugging in L into the plane equation: 50:42 - Equation of the bottom clipping plane: 58:52 - Plugging in L into the plane equation: 1:01:04 - Summary: Line is clipped at left and top clipping planes: 1:03:08 This video was taken from my earlier video listed below: - Laboratory Project: Putting 3D in Perspective: https://youtu.be/3txedAqdtkQ - HIVE video notes: https://peakd.com/hive-128780/@mes/laboratory-project-putting-3d-in-perspective - Video sections playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0ElsrMs_IBprUoHocIwyAmK Related Videos: Sequences and Series playlist: https://www.youtube.com/playlist?list=PLai3U8-WIK0FjJpwnxwdrOR7L8Ul8VZoZ . ------------------------------------------------------ SUBSCRIBE via EMAIL: https://mes.fm/subscribe DONATE! ʕ •ᴥ•ʔ https://mes.fm/donate Like, Subscribe, Favorite, and Comment Below! Follow us on: MES Truth: https://mes.fm/truth Official Website: https://MES.fm Hive: https://peakd.com/@mes MORE Links: https://linktr.ee/matheasy Email me: contact@mes.fm Free Calculators: https://mes.fm/calculators BMI Calculator: https://bmicalculator.mes.fm Grade Calculator: https://gradecalculator.mes.fm Mortgage Calculator: https://mortgagecalculator.mes.fm Percentage Calculator: https://percentagecalculator.mes.fm Free Online Tools: https://mes.fm/tools iPhone and Android Apps: https://mes.fm/mobile-apps