integral dari : ∫ cos^4 x dx
Posted by andi telaumbanua on Feb 17, 2018 in Matematika |
Tentukanlah integral dari : ∫ cos^4 x dx
Jawab:
∫cos ^n u du = (cos^(n-1) u sin u) / n + (n-1) /n ∫ cos^(n-2) u du + c
Maka:
∫ cos^4 x dx = (cos^3 x sin x) /4 + (4-1) /4 ∫ cos^2 x dx
∫ cos^4 x dx = (cos^3 x sin x) /4 + 3/4 ( ( cos x sin x) /2 + (2-1)/2 ∫ (cosx)^(2-2) dx )
∫ cos^4 x dx = (cos^3 x sin x) /4 + 3/4 ( ( cos x sin x) /2 + 1/2 ∫ (cosx)^0 dx )
∫ cos^4 x dx = (cos^3 x sin x) /4 + 3/4 ( ( cos x sin x) /2 + 1/2 ∫ dx )
∫ cos^4 x dx = (cos^3 x sin x) /4 + 3/4 (( cos x sin x) /2 + 1/2 (x) ) + C
∫ cos^4 x dx = (cos^3 x sin x) /4 + ( 3 cos x sin x) /8 + 3/8 x + C
