ContohSoal Integral Eksponensial. Pada postingan ini kita membahas contoh soal integral tak tentu dan penyelesaiannya atau pembahasannya. Sejumlah dana yang disimpan di bank dengan bunga majemuk kontinyu akan tumbuh secara kontinyu sesuai fungsi p t = p 0. Integral tak tentu suatu fungsi f (x) ditulis dengan ∫ f (x) dx, yaitu operasi yang
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sin⁵x dx = ∫ (sin²x) dx = ∫ (1-cos²x)².sin x dx = ∫ (1 - 2.cos²x + cos⁴x).sin x dx Berikan substitusi: u = cos x du = -sin x dx Yang memberikan: sin x dx = - du Sehingga menjadi: = ∫ (1 - 2u² + u⁴) (-du) = ∫ (-1 + 2u² - u⁴) du = -u + 2/3 u³ - 1/5 u⁵ + C Substitusikan ulang u = sin x
$\begingroup$ 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 .
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Tentukanhasil dari ∫ (x 3 + 2) 2. 3x 2 dx = .. Penyelesaian : Misal u = x 3 + 2. du = 3x 2 dx. dx = du / 3x 2. ∫ (x 3 + 2) 2. 3x 2 dx; ∫ u 2. 3x 2 du / 3x 2; ∫ u 2 du; Jadi, jawabannya adalah Demikian penjelasan mengenai soal - soal integral semoga dapat meningkatkan pemahaman kalian dalam belajar dan mengerjakan soal. Semoga
Haisobat matematika! Sebelum Anda melanjutkan tentang bahasan logaritma natural, silahkan Anda pelajari dahulu bahasan logaritma di sini. Ingatkah Anda pada aturan pangkat umum di bahasan topik integral?Kalau tidak ingat mari saya bangunkan.hehe
integralx^-4 (x+5)^2 dx adalah Tanya. 11 SMA. Matematika. KALKULUS.
A. cos x - B sin x . d y dx 2 2 = - A Sin x - B cos x . d y dx 2 2 = - (A Sin x + B cos x) Jadi . d y dx 2 2 = - y atau . d y dx y 2 Artinya X dan Y mempunyai pangkat yang derajatnya sama , yaitu 1. (Penggunaan Faktor Integral) Bentuk umum dari Persamaan Linier Orde Pertama adalah . dy dx +py =Q. Contoh1 : x dy dx +y =x. 3.
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integral sin pangkat 5 x dx
