Not a specific question, but i need help with integrals, like I get the basic stuff, but when the integrals get more complicated with say trig functions, I get confused.

Question

anonymous · Answer

what do you not get

anonymous · Answer

like the int of cos2xdx is (1/2)sin2x
that is confusing to me

anonymous · Answer

in that sort of case and in others similar, where you have a modified base function, when you use the substitution method to integrate, that 1/2 in this case comes from the fact that in order to make a substitution for 2x, you have to sub in the dx of the integral, and that is by taking the derivative of 2x, so it ends up becoming 2dx. You don't have a 2dx in the integral, but if you were to put it in there by multiplying 2, you have to put also 1/2 so as not to change the integral. So you in this case say let 2x=u, du= 2dx, then your integral becomes (1/2)the integral of cos u du. which then solves to the -1/2sin(2x) once you integrate and put the substituted variable back in.

anonymous · Answer

It is the same with all kinds of other variations in base functions, a person has to make a substitution and manipulate the integral to solve for a true answer. Then there are other techniques that are simlarly used for mor complicated instances

anonymous · Answer

okay, I think I understand a little more thank you

anonymous · Answer

no problem, look up u substitution in your text and you will have more examples too.