$\begingroup$ First off, not going to lie, this is for an assignment. Basically, we're given the integral $$\int \sin^5x\,dx$$ and rewritten form of $$\int [A \sinx + B \sin x \cos^2 x+C\sinx\cos^4x]\,dx$$ using certain trigonometric Identities. We're required to find the values of $A$, $B$ and $C$. Now for the life of me I can't find a set of transformations that will give me that transformation. The power reducing formula gets me to $$\int 5/8\sin X - 5/16\sin3X + 1/16\sin5X $$ and then I can use the multiple angles identity on $\sin3x$ and $\sin5x$, and then I use the power Identities again on the resultant and I just seem to keep going in circles, unable to get the transformation asked for and answer the question. Please send help! egreg235k18 gold badges137 silver badges316 bronze badges asked Sep 23, 2016 at 951 $\endgroup$ 0 $\begingroup$ This is easy. Notice that $$\sin^5 x = \sin x \sin^4 x = \sin x 1- \cos^2 x^2 = \sin x 1 - 2 \cos ^2 x + \cos^4 x ,$$ so $A = 1, \ B = -2, \ C = 1$. Integration, then, is easy, because $$\int \sin x \cos^n x \ \Bbb d x = - \int \cos x' \cos^n x \ \Bbb d x = \frac {\cos^{n+1} x} {n + 1} .$$ answered Sep 23, 2016 at 959 Alex gold badges47 silver badges87 bronze badges $\endgroup$ 2 $\begingroup$Hint You want to find values for $A,B$ and $C$ such that, for all $x$, we have that $$\sin^5x=A\sin x+B\sin x\cos^2x+C\sin x\cos^4x.$$ So try to plug there some specific values, such as $x=\tfrac\pi2$, to solve for $A,B$ and $C$. answered Sep 23, 2016 at 955 WorkaholicWorkaholic6,6332 gold badges22 silver badges57 bronze badges $\endgroup$ You must log in to answer this question. Not the answer you're looking for? Browse other questions tagged .
³kfk³ f(x )dx (ii) ³ f (x ) g (x )dx ³ f (x )dx ³ g (x )dx Latihan : Cari integral tak tentu berikut : a. ³x 3 x 1 dx b. ³(y 4y)2 dy c. dx x x 3 3x 2 1 ³ d. ³3sin 2cost dt e. dx x x x n 2c 3n2 ³ Teorema 4 : Substitusi Integral Tak Tentu Misal g adalah fungsi yang dapat diturunkan dan F adalah suatu anti turunan dari f. Jika u g(x) maka
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SatuBatas Tak Terhingga. Perhatikan fungsi f (x) = xe−x f ( x) = x e − x dan integral dari ∫1 0 xe−xdx ∫ 0 1 x e − x d x atau ∫ 2 0 xe−xdx ∫ 0 2 x e − x d x atau ∫ b 0 xe−xdx ∫ 0 b x e − x d x, di mana b adalah sebarang bilangan positif. Seperti yang bisa anda lihat pada Tabel 1 di bawah, ketika kita meningkatkan
Penjelasantentang contoh soal integral tentu, tak tentu, substitusi, parsial, trigonometri beserta pengertian dan jenis-jenis integral dan pembahasannya variabel pada suatu fungsi mengalami penurunan pangkat. Berdasarkan contoh itu, diketahui bahwasanya ada banyak fungsi yang mempunyai hasil turunan yang sama yaitu yI = 3×2. Fungsi dari
integralx^-4 (x+5)^2 dx adalah Tanya. 11 SMA. Matematika. KALKULUS.Dengancara serupa diperoleh rumus reduksi untuk ∫sinnx dx, yaitu : sinnx dx sinn cos sinn n x x n n = − + x dx − − − ∫ ∫ 1 1 1 2 Contoh cos3 cos2 sin cos cos2 sin sin 1 3 2 3 1 3 2 3 ∫ x dx = x x + ∫ x dx = x x + x +C Integral bentuk ∫sinmx cosnx dx dengan m,n ˛ B+. Bila m atau n merupakan bilangan ganjil maka untuk suku.
integral sin pangkat 5 x dx
