Integral dari ∫ sin^4 x cos^3 x dx
Posted by andi telaumbanua on Feb 17, 2018 in Matematika |
Tentukanlah Integral dari :
∫ sin^4 x cos^3 x dx
Jawab:
Misalkan: u = sin x
Maka: du/dx = cosx
Sehingga: dx = du/cosx
∫ sin^4 x cos^3 x dx = ∫u^4 cos^3 x du/cosx
∫ sin^4 x cos^3 x dx = ∫ u^4 cos^3 x (du/cos x)
∫ sin^4 x cos^3 x dx = ∫ u^4 cos^2 x du
Karena: cos^2 x = 1 – sin^2 x
Maka:
∫ sin^4 x cos^3 x dx = ∫ u^4 (1- sin^2 x) du
Karena: u = sin x
Maka:
∫ sin^4 x cos^3 x dx = ∫ u^4 (1- u^2) du
∫ sin^4 x cos^3 x dx = ∫ (u^4- u^6) du
∫ sin^4 x cos^3 x dx = 1 /(4+1) u^(4+1) – 1 /(6+1) u^(6+1) + C
∫ sin^4 x cos^3 x dx = 1 /5 u^5 – 1 /7 u^7 + C
∫ sin^4 x cos^3 x dx = 1 /5 sin^5 x – 1 /7 sin^7 x + C
kurang paham;(
bagian mana?