Question

evaluate this integral

integral (1-cos t/2)^2 sin t/2 dt

u= 1-cos t/2

Answer 1

if u=1-cos(t/2) then du=1/2 *sin(t/2) dt or 2du=sin(t/2) dt

Answer 2

so now we have \[2\int\limits_{}^{}u^2du\]

Answer 3

thats the part i don't get

Answer 4

how to get du

Answer 5

so you are having trouble with derivatives?

Answer 6

the derivative of 1 is 0 and the derivative of -cos(t/2) is 1/2(-1)(-sin{t/2})=1/2 sin(t/2)

Answer 7

u is a function of t so we have du/dt=1/2*sin(t/2) so by multipling dt on both sides we have du

Answer 8

ok i understand now thanks!