Question

Question about the substitution method. Medals!

I was wondering why taking the first and second step remove 3(t)^2 by taking the derivative. Does 6t just turn into an arbitrary constant thereby negating itself?

Answer 1

as opposed to

Answer 2

\[(t ^{3}+4)=u \]
\[then\]
\[du/dt=3t ^{2}\]
now \[du=3t ^{2}dt\]
then replace the values and do normal integration.. hope it will help you.. thank you..

Answer 3

2nd one try in same way.. if you dont understand then tell me..

Answer 4

but after du=3t^2 it disappears, is that because it becomes a constant? I know that the u^5 becomes u^6/6 but I can't see you du would fit in.

Answer 5

no actually (t) is a variable.. and we replacing it by another variable for the shake of easy calculation.. its not a constant..

Answer 6

replacing t with d(u) which is a dummy variable, what about the second question with sqrt(4x-5) why does the dummy variable = (1/4)du when for 3t^2 neq 6du

Answer 7

while for*

Answer 8

hang on for one minute...

Answer 9

ok

Answer 10

is it helful or not?

Answer 11

very helpful, really helps to see it on paper. thanks so much (: