Catatan Integral part II

ket: ^=pangkat^2=pangkat 2ln=logaritma naturaltan^(-1) x= arc tan x ∫u du = (1/2) u^2 + C∫u dv = uv - ∫v du∫u^n du = (1/(n+1)) u^(n+1) + C∫(1/u) du = ln |u| + C∫e^u du = e^u + C∫a^u du = (a^u)/(ln a) + C∫sec^2 u du = tan u + C∫csc^2 u du = -cot u + C∫sec u tan u du = sec u + C∫csc u cot u du = - csc u + C∫tan u du = ln |sec u| + C∫cot u du = ln |sin u| + C∫sec u du = ln |sec u + tan u| + C∫csc u du = ln |csc u - cot u| + C∫sin^ u du = u/2 - (sin 2u)/4 + C∫cos^2 u du = u/2 + (sin 2u)/4 + C atau ∫cos^2 u du = ∫(1/2)(1+cos 2u) du∫tan^2 u du = (tan...

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rumus tercepat deret kombinasi

Tahukah anda bagaimana cara menentukan hasil dari deret kombinasi berikut ::4C1 + 2(4C2) + 3(4C3) + 4(4C4) ???6C1 + 2(6C2) + 3(6C3) + 4(6C4) + 5(6C5) + 6(6C6) ???atau mungkin 99C1 + 2(99C2) + 3(99C3) + .................98(99C98) + 99(99C99) ???Caranya, gunakan rumus d * 2^(d-1) ^_^4C1 + 2(4C2) + 3(4C3) + 4(4C4) = 4 + 4.3 + 4.3 + 4 = 32Nah, sekarag kita coba buktikan dgn rumus tadi, maka::d = 44 * 2^(4-1) = 32gimana ? hasilnya sama kan ? ^_^6C1 + 2(6C2) + 3(6C3) + 4(6C4) + 5(6C5) + 6(6C6) = 6 + 6.5 + (6.5.4)/2! + (6.5.4)/2! + 6.5 + 6 = 1926 *...

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GENERATING FUNGTION

Rumus-Rumus penting pada generating fungtion: 1) 1+x+x"+x"'+....x^n=(1-x^(n+1))/(1-x)2) 1+x+x"+.......=1/(1-x)3) (1+x)^n=1+C(n,1)x+C(n,2)x"+...+C(n,r)x^r+...+C(n,n)x^n4) (1-x^m)^n=1-C(n,1)x^m+C(n,2)x^(2m)+....+(-1)^r(C,r)x^(rm)+...+(-1)^n C(n,n)x^(nm).5)1/(x-1)^n=[(sigma (0 sampai tak hingga)) x^i]^n=(sigma (0 sampai tak hingga)) C(n+i-1, i) x^i6) Jika h(x)=f(x).g(x), dimana f(x)=a0+a1x+a2x^2+.... dan g(x)=b0+b1x+b2x^2+.... makah(x)=a0b0+(a1b0+a0b1)x+(a2b0+a1b1+a0b2)x^2 + .... +(arb0+a_r-1 . b1+a_r-2 . b2+.....(a0br)x^r.7. Koefisien x^r pada (1+x+x"+...)^n...

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