Question

1AM stress!!! UGH!! help!
dx/dt = (ct-1)^1/2 , c= constant
i know i have to integrate but how do you integrate the (ct-1)^1/2???

Answer 1

make substitution let ct-1 = y

Answer 2

then what?

Answer 3

Then Integrate y^(1/2) like you normally would.

Answer 4

Add one to the power (so it becomes (3/2) and divide by the new power (so you are dividing by 3/2 which is the same as multiplying by 2/3).

Answer 5

i did it and i got 2/3(ct-1)^3/2 + c?

Answer 6

Remember that you have to multiply by the derivative of the (ct-1) as per the chain rule, so you need to multiply by c as well.

Answer 7

oh so am i correct?

Answer 8

What am I doing? Go back a step. Let u = (2t-1)

Answer 9

are we using u subsitution?

Answer 10

oh where did 2 come from?

Answer 11

?? where did 2 come from?

Answer 12

how come? isnt c constant?