Tentukan f(x) jika f'(x) = 5 cos x + 4 sin x , f (π/2) = 3

Tentukan integral fungsinya:
f(x)
= Int f'(x) dx
= Int 5 cos x + 4 sin x dx

Perlu diingat:
Int sin x dx = -cos x + C
Int cos x dx = sin x + C

Sehingga menjadi:
= Int 5 cos x dx + Int 4 sin x dx
= 5. Int cos x dx + 4. Int sin x dx
= 5.sin x + 4(-cos x) + C
= 5sin x – 4cos x + C

Dengan f(π/2) = 3
3 = 5sin π/2 – 4cos π/2 + C
3 = 5(1) – 4(0) + C
3 = 5 – 0 + C
3 = 5 + C
C = -2

Sehingga:
f(x) = 5 sin x – 4 cos x – 2