Hello
Let . Then, you know and you're looking for which simply is the derivative of a composite function.
I don't know...is there a specific terminology for this type of problem
d/dx of the integral from 0 --> x^2 of sin^2t * dt
can you guys understand that. i don't know how to do that fancy synthax.
and the question i have about this was whether there was some kind of trick to this problem and is there a specific terminology for this type of problem so i can study up further.
Maybe this will help...
let
by the fundemental theorem of Calculus we get
so for example
then
now back to your function
let
the problem is your upper limit of integration is not linear so we need to fix it up the the FTC applies
let
then
now using the chain rule and the FTC we get
now we need to sub the value of u back in and we get