Master practical applications of integral calculus through this comprehensive video playlist covering essential techniques for solving real-world problems across multiple disciplines. Explore fundamental concepts including calculating areas between curves using both dx and dy methods, determining arc length for various functions, and finding average values of functions. Learn volume calculation methods through disk, washer, and cylindrical shell techniques for solids of revolution about different axes. Discover surface area calculations for surfaces of revolution and apply numerical methods like Simpson's rule for complex integrations. Delve into physics applications including work problems with variable forces, elastic springs, and rope lifting scenarios, plus motion analysis through rectilinear and vertical motion problems. Study mechanics concepts such as moments of systems, center of mass calculations, hydrostatic pressure and force problems, and centroids of plane regions. Examine economics applications through present and future value calculations with continuous compounding, consumer and producer surplus analysis, and various financial modeling scenarios. Explore probability applications with density functions and biological applications including cardiac output calculations and Poiseuille's law for fluid flow. Apply advanced geometric concepts through the Theorem of Pappus and triangle area calculations using coordinate geometry, providing a thorough foundation for applying integral calculus across engineering, physics, economics, and biological sciences.

Syllabus

Applications of Integration (KristaKingMath)
Average Value of a Function Example 1 (KristaKingMath)
Area between curves - dx (KristaKingMath)
Area between curves - dy (KristaKingMath)
Area between curves - sketching (KristaKingMath)
Arc Length (KristaKingMath)
Arc length x=g(y) (KristaKingMath)
Arc length - simpson's rule (KristaKingMath)
Surface Area of Revolution (KristaKingMath)
Surface area of revolution - simpson's rule (KristaKingMath)
Surface of Revolution (KristaKingMath)
Volume of rotation: disk method about the y-axis or x= (KristaKingMath)
Volume of rotation: disk method about the y-axis or x= (KristaKingMath)
Volume of rotation: disk method about the x-axis or y= (KristaKingMath)
Volume of rotation: washer method about the x-axis or y= (KristaKingMath)
Volume of rotation: washer method about y-axis or x= (KristaKingMath)
Volume of rotation: washer method about x-axis or y= (KristaKingMath)
Volume of rotation: cylindrical shells about the y-axis or x= (KristaKingMath)
Volume of rotation: cylindrical shells about the y-axis or x= (KristaKingMath)
Volume of rotation: cylindrical shells about the x-axis or y= (KristaKingMath)
Mean value theorem for integrals (KristaKingMath)
Work done using a rope to lift a weight (KristaKingMath)
Work Done on Elastic Springs (KristaKingMath)
Work Done by a Variable Force (KristaKingMath)
Moments of the system (KristaKingMath)
Moments of the system, x-axis (KristaKingMath)
Center of mass of the system (KristaKingMath)
Center of mass of the system, x-axis (KristaKingMath)
Hydrostatic pressure (KristaKingMath)
Hydrostatic force (KristaKingMath)
Vertical Motion (integration) (KristaKingMath)
Rectilinear Motion (KristaKingMath)
Centroids of Plane Regions (KristaKingMath)
Centroid of the plane - simpson's rule (KristaKingMath)
Area of the triangle with the given vertices (KristaKingMath)
Present and Future Value (KristaKingMath)
Present and Future Value Example 2 (KristaKingMath)
Present and Future Value Example 3 (KristaKingMath)
Present and Future Value Example 4 (KristaKingMath)
Present and Future Value Example 5 (KristaKingMath)
Consumer and Producer Surplus (KristaKingMath)
Probability density functions (KristaKingMath)
Cardiac output (KristaKingMath)
Cardiac output - simpson's rule (KristaKingMath)
Poiseuille's law (KristaKingMath)
Theorem of Pappus (KristaKingMath)
Present value of a single deposit, compounded continuously - How do you find it?