This week in AP calc we learned about some more u substitution. It helped me do some integrals. I also mastered one of my quizzes.
Let me walk you through some U substitution. Hmm, I'm feeling like finding the area under the curve made by the equation y=tanxsec^2x from the interval [-pi/4,0]. That sounds great. So, instead of trying to mess with a lot of reverse chain rule things let's just relabel tanx as "u". u = tanx. Then get the derivative of that. du=sec^2dx. Ayy lmao look back at the integral. We have usec^2dx so let's replace with du. Now we have the integral of u du. That's easy. The anti derivative of u is simply u^2/2. Then we plug in tanx back in then we use the fundamental theorem of calculus to find the area. F(a)-F(b)