Explore advanced calculus concepts through a comprehensive series of lectures covering applications of antiderivatives, fundamental theorem of calculus, definite and indefinite integrals, u-substitution, area between curves, work problems, integration by parts, trigonometric integrals, and various techniques of integration. Delve into real-world applications such as car braking with constant deceleration and pumping water from spherical tanks. Practice solving complex problems from Stewart Calculus and prepare for integration competitions with challenging examples.
Overview
Syllabus
A Car Brakes with a Constant Deceleration:: Find Initial Velocity :: Applications of Antiderivatives.
Fundamental Theorem of Calculus Part 1 :: Finding Derivatives.
Definite Integral of Piecewise Function.
Indefinite Integral of x^(1/3) + 1/(x^(1/3)).
Indefinite Integral of ((1+r)/r)^2.
Integral of (x-1)e^((x-1)^2) :: U Substitution :: Explicit Substitution.
Integral of x/sqrt(1+2x) from 0 to 4 | U Substitution | Explicit Substitution.
Find the Area Between the Curves | y = cos(x) and y = 2-cos(x).
Amount of Work to Pump Water Out of a Spherical Tank With 3 Meter Radius.
Integration by Parts :: Integral of arctan(1/x) from 1 to sqrt(2)..
Integral of csc^5(theta) cos^3(theta) :: Trigonometric Integrals.
Trigonometric Substitution Definite Integral :: sqrt(1-4x^2).
Integral of sec^2(y) cos^3(tan(y)) :: Trigonometric Integrals.
Stewart Calculus Section 7.5 Odd Problems #9-31 :: Techniques of Integration Examples.
Stewart Calculus 7th Edition Section 7.5 :: Even Problems 2 - 32.
∫x^2 dx from 0 to 1... Using a different approach!.
2021 Integration Bee Integral.
Taught by
Jonathan Walters
