<p>okay i'm selfstudying calculus right now and i'm doing very well. i just have a specific concept i dont get. right now i'm into integrals, and the concepts so far about what it is and where it came from and how to use the power rule are all good. however, something about U-Substitution is really bothering me. i can do u-substitution almost automatically, cuz i follow the rules and such, so i dont have a mathematical problem. HOWEVER, when you find
"du" = ... "dx", why is it that u can SUBSTITUTE the "du" into the "dx" symbol of the original problem. i thought for integrals, the dx is simply a notation or symbol meaning with respect to x and integrate. what math concept allows me to substitute that dx when its just a symbol for integrating ! help plz, be thorough</p>
<p>no it is a symbol representing a very very very very very small amount at least according to my math teacher. you can basically do it for the same reason that you can use separation of variables for diff eqns. i had the same question this year and this is basically what he told me. i am not sure if i understand 100% but it kind of makes since. someone can probably do a better job explaining.</p>
<p>now???!!!???!!??!</p>
<p>anyone else</p>
<p>Look at it like this. Take the function ((2x+3)^4)dx. If you wanted to do a u-sub to interate, you would do this:</p>
<p>((2x+3)^4)dx=
(u^4)dx</p>
<p>However, then you have a problem. The variables don't match. You have a u, but a dx. You need a du, since you are integrating a function in terms of u. Thus, you solve for du.</p>
<p>2x+3=u
2dx=du
dx=du/2</p>
<p>(u^4)(du/2) -> integrate
(u^5)/10 -> sub back in
((2x+3)^5)/10</p>
<p>Now you can do the problem, since the variable you are integrating, u, is paired with a du. Basically the point is, when you switch variables, you have to switch all of them. Im not really sure if this answered your question, but I hope it helped.</p>
<p>OKAY i have another question i was just wondering at. is it useful to memorize the unit circle ????????????</p>
<p>no put it on the calc</p>
<p>how heavy is it tho ? like is there a lot of trig with exact values answers n such</p>
<p>Like the unit circle is hard to memorize?
S l A
<strong>l</strong>
T l C All students take calculus
...l
0/2, 2/2
1/2, Rad(3)/2
rad(2)/2 , rad(2)/2
rad(3)/2, 1/2
2/2, 0/2</p>
<p>then go negative. Its not hard</p>
<p>what about trig indentities, functions of sum, difference, half angle , double angle, etc</p>
<p>^do i have to memorize them by heart in order to be successful in calc ?</p>
<p>If you study enough, you will have them memorized anyway. The double angle formula shows up sometimes, usually when working with polar coordinates. The half-angle formula is rarely seen.</p>