This course on Trigonometric Substitution in Calculus aims to teach students how to integrate expressions involving square roots and trigonometric functions. By the end of the course, students will be able to integrate various types of expressions, such as sqrt(x^2+1), sqrt(x^2-1), and sqrt(1-x^2), using trigonometric substitution techniques. The course covers topics like x=a*sinθ, x=a*secθ, and x=a*tanθ for integration purposes. The teaching method involves solving specific integration problems step by step. This course is intended for students studying Calculus 2 who want to deepen their understanding of integration techniques involving trigonometric substitution.
Overview
Syllabus
Integral of sqrt(x^2+1), integral of sqrt(x^2-1), integral of sqrt(1-x^2).
Trig substitution integration: x=a*sinθ, calculus 2.
Trig substitution integration: x=a*secθ, calculus 2.
Trig substitution integration: x=a*tanθ, calculus 2.
integral of 1/sqrt(x^2+16).
integral of sqrt(1-4x^2) ,Trig Substitution.
integral of sqrt(x^2-9)/x^3 by trig substitution.
integral of sqrt(x^2+2x).
integral of x*sqrt(1-x^4).
integral of sqrt(1+x^2).
Q53, integral of sqrt(x^2-1).
integral of sqrt(1-x^2).
integral of 1/(x^2*sqrt(x^2-1), via trig sub.
Q53, Integral of 1/(t^2*sqrt(t^2-16)), trig sub.
integral of 1/(a^2+x^2).
Q56, integral of sqrt(1+x^2)/x vs integral of x/sqrt(1+x^2).
Taught by
blackpenredpen
