Help Needed (1 Viewer)

[NBGHHS]

Im not sturggling with three unit, but i do find myself stuck at questions a lot. (fitzpatrick three unit)


\int Sin^2 ( \frac{x}{2}) \, dx

and, does anyone know where i can find J.B Fitzpatrick three unit maths worked solutions?
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[Nooblet94]

Here's two hints: use the substitution u=x/2 and find sin^2(u) in terms of cos(2u)

 

[Timske]

^ you can do it by substitution but this is how i would do it without substitution

int sin^2 (x/2) dx

sin^2(x) = 1/2(1-cos2x)
:. sin^2(x/2) = 1/2(1-cosx)

:. int sin^2 (x/2) dx = int 1/2(1-cosx)

= 1/2 int 1-cosx
= 1/2(x - sinx) + c
= x/2 -1/2(sinx) + c