Question

please help.
photo attcahed.
i have no idea what i have to do.

Answer 1

make a u substitution

Answer 2

backwards

Answer 3

the questions are seems different from substitution questions :/

Answer 4

that is because the substitution is backwards

Answer 5

could you show me the steps for A so i may do questions B and C for myself?

Answer 6

yeah i am trying to think of a good way to write it, hold on a second

Answer 7

thank you,

Answer 8

damn let me start again
the point is, we want to convert the inside piece to \(t\)

Answer 9

we can do this,
put u= 2t
then use the property that definite integral remain same with variable change, 'change of variable' property.

Answer 10

think of it as \[\int f(g(x))dx\] we want \[\int f(x)\] so we have to find \(g^{-1}(x)\) to convert back
in the case \(f(1-4t)\) if you set \(x=1-4t\) you get \(t=\frac{1-x}{4}\)

Answer 11

that is the substitution you want to make

Answer 12

@hartnn i think you have to go the other way, put \(u=\frac{t}{2}\)

Answer 13

hmmm...i was saying this :
\(\int \limits_0^{0.5}f(2t) dt= \int \limits_0^{0.5}f(2u) du \\put \quad 2u=t, \\ =(1/2)\int \limits_0^1f(t)dt \)
so, in 2nd case , you can do 1-4u =t

Answer 14

no need for inverse function stuff...i think
1-4u = t
-4du = dt
du = dt/(-4) .....this is same thing you will get after finding inverse function ...

Answer 15

i am confused...