In this lecture you will learn Trigonometric Substitutions. Professor Murray will go over the fundamental idea of substituting in Calculus integration problems with examples that help you remember 'du' and 'dx.'
Remember to make the
substitution as well as the main substitution.
can sometimes use trigonometric substitution even when you dont
have a square root.
However, in these cases, you should only be using the tangent
substitution. If you get one of the other ones, then you should have
been able to factor the algebraic expression, and trigonometric
substitution was not necessary.
If you have a linear term (x or u, as opposed to x² or
u²), complete the square and make a substitution to eliminate the
linear term before you make the trigonometric substitution.
If the coefficient of the quadratic term (x²) is negative,
factor the negative out of all terms before completing the square.
you make the trigonometric substitution, it becomes a trigonometric
integral that you can handle using the techniques in the previous
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.