Question

Ada yang bisa nomer 33?

Answer 1

Batasnya tidak saya tuliskan, ya.

Ingat :
cos(2x) = cos²x - sin²x
cos(2x) = (1 - sin²x) - sin²x
cos(2x) = 1 - 2sin²x
2sin²x = 1 - cos(2x)
sin²x = (1 - cos(2x))/2

∫(sin²x + sin(2x)) dx = ∫((1 - cos(2x))/2 + sin(2x) dx
= ∫1/2 - cos(2x)/2 + sin(2x) dx
= (1/2)x - (1/4)sin(2x) - (1/2)cos(2x) )

= [ (1/2)(π/2) - (1/4)sin(2.π/2) - (1/2)cos(2.π/2)] - [(1/2)(0) - (1/4)sin(0) - (1/2)cos(0)]

= [π/4 - 0 - (1/2)(-1) ] - [0 - 0 - 1/2(1)]
= π/4 + 1/2 +1/2
= π/4 + 1
= 1 + π/4