Why does u-substitution give the wrong coefficient for ∫sin⁴(3t)dt?

[camboguy]

Homework Statement

intergral from pi to 0.
of
(sin(3t)dt)^4

The Attempt at a Solution

okay so i know how to do this but when i tried substitution putting 3t=u and (1/3)du= dt i always came with the the wrong coefficient at the end with the answer and so i would multiply it wrong. but then when i do not use u/du substitution everything works well? why is that? what is the difference? and I am using u/du substitution improperly or something?

 

[rootX]

Are you correctly changing the limits?

 

[camboguy]

i didn't need to change it because i just plugged back in the variables u with 3t. just wondering it should be correct even if i substitute right?