Calculus 1

Dive into a comprehensive calculus lecture covering essential topics in antiderivatives, integration techniques, and applications. Learn to find antiderivatives, apply u-substitution for complex integrals, and understand the Fundamental Theorem of Calculus. Practice solving definite and indefinite integrals, including piecewise functions and fractional exponents. Explore practical applications such as finding areas between curves, calculating work in pumping water, and solving velocity problems in physics. Master these fundamental calculus concepts to build a strong foundation for advanced mathematical studies.

Find the Function f :: Antiderivatives.
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.
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.
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.
A Car Brakes with a Constant Deceleration:: Find Initial Velocity :: Applications of Antiderivatives.