ANOTHER way to integrate (oh joy!!) Trig Substitutions ANOTHER way to integrate (oh joy!!)

Again, when it doesn’t fit anything we’ve done before… Such as something that looks familiar but isn’t really exactly what we need For example, looks sort of like sin-1 or sec-1, but its not quite right (why?) What to do? I thought you’d never ask…. 

Label a triangle Don’t worry “how” x Θ 3 Therefore 1. 2. Then

Ok, that I follow, but how did you label that triangle? These are the substitutions to remember: x a a x x a

Are these the only possibilities? No – we could come up with other configurations easily. BUT, if we use cosine, cotangent or cosecant we then introduce negatives. Hint: Make a notecard for yourself (the previous slide) and look at the basic form to decide the substitution.

Examples (#9 from HW)