Integral of sin x 3 is an interesting and complex mathematical concept. It involves taking the integral of a trigonometric function, sin x, and multiplying it by 3. This is an important concept to understand in mathematics, as it can be used to solve many problems. Integral of sin x 3 can be used to find the area under a graph of the function. To do this, you must first calculate the integral of sin x, which is the same as the area under a graph of sin x. After this, you must multiply the integral by 3. This will give you the area under the graph of sin x 3. Integral of sin x 3 can also be used to find the volume of a solid of revolution. To do this, you must first calculate the integral of sin x, then divide the integral by 3. This will give you the volume of the solid of revolution. Integral of sin x 3 can also be used to find the centroid of a surface of revolution. To do this, you must first calculate the integral of sin x, then multiply the integral by 3. This will give you the centroid of the surface of revolution. Integral of sin x 3 can also be used to find the length of a curve. To do this, you must first calculate the integral of sin x, then multiply the integral by 3. This will give you the length of the curve. Integral of sin x 3 is an important concept in mathematics, as it can be used to solve many problems. It is important to understand how to calculate the integral of sin x, as well as how to multiply it by 3. This will help students to understand the concept and use it to solve problems.
Questions and Answers:
1. 1. integral ( Sin x + Cos x ) dx2.integral (X*2 - 2 Sin x) dx3. integral ( Sin x Cos*2 x )dx4. integral ( 3 Sin x-4 Cos x) dx
Penjelasan dengan langkah-langkah:
1)
[tex]\int( \sin(x) + \cos(x) )dx \\ = \int \sin(x) dx + \int\cos(x) dx \\ = - \cos(x) + \sin(x) + c \\ = \sin(x) - \cos(x) + c[/tex]
2)
[tex]( {x}^{2} - 2 \sin(x) )dx \\ =\int {x}^{2} dx - 2\int \sin(x) dx[/tex]
[tex] = \frac{2}{3} {x}^{3} + 2\cos(x) + c [/tex]
3)
[tex] \int(\sin(x) \cos^{2}(x) )dx [/tex]
misal
u = cos x
du = -sin x dx
[tex]dx = \frac{du}{ - \sin(x) } [/tex]
[tex] = \int\sin(x) {u}^{2} \frac{du}{ - \sin(x) } \\ = - {u}^{2} du \\ = - \int \frac{ {u}^{3} }{3} + c \\ = - \frac{1}{3} \cos ^{3} (x) + c[/tex]
4)
[tex]\int(3 \sin(x) - 4 \cos(x) )dx \\ = 3 \int\sin(x) dx - 4 \int\cos(x) dx \\ = 3( - \cos(x) ) - 4( \sin(x) ) + c \\ = - 3 \cos(x) - 4 \sin(x) + c[/tex]
2. integral 4 sin 5x sin x dx integral cos 3x cos x dx integral 3 sin 2x dx
= integral 2 (sin6x+cos4x) dx , integral 1/2(cos4x +cos 2x) dx, 3 integral sin2x dx
3. integral trigonometri: 1. integral sin x cos^2 x dx 2. integral sin^4 x cos^3 x dx
Tadi kburu eror jaringannya ... Maaf ya ..jawabn l kdua baru kekirim
4. integral x^2 . sin x^3 dx
∫x² sin(x³+π) dx
=∫ x² sin(π+x³) dx
=∫ x² (-sin x³) dx
=-∫ x² sin x³ dx
misal u=x³
maka du/dx = 3x²
sehingga du/3 = x² dx
=-∫ sin u (du/3)
=-⅓ ∫ sin u du
=-⅓ (-cos u)
=⅓ cos x³ + C
5. 1. integral sin¹⁰xcosxdx2. integral (x²/3+3)²x²dx
Penjelasan dengan langkah-langkah:
1. integral sin¹⁰xcosxdx
Soal ini dapat diselesaikan dengan pemisalan
Misal:
u = sinx
Turunkan kedua sisi
du = cosx dx
Sehingga dx = du/cosx
Subsitusikan ke persamaan awal
integral sin¹⁰cosxdx
=integral u¹⁰cosx(du/cosx)
nilai cosx bisa habis
=integral u¹⁰du
dengan integral biasa diperoleh
(1/11)u^(11) + C
dimana u adalah sinx
2xSehingga:
integral sin¹⁰xcosxdx = (1/11)sin^11(x) + C
2. integral (x²/3+3)²x²dx
(x²/3+3)²x²= (x^4/9 + 2x^3 + 9)(x^2)
= x^6/9 + 2x^5 + 9x^2
integral x^6/9 + 2x^5 + 9x^2
=(1/9)*(1/7)x^7 + 2*(1/6)x^6 + 9*(1/3)*x^3 + C
= (1/63)x^7 + (1/3)x^6 + 3x^3 + C
Semoga membantu
6. integral x^3 sin x dx
x³ sin x dx =
J = ∫ x³ sin x dx = - ∫ x³ d(cos x)
J = -x³ cos x + ∫ 3x² cos x dx = -x³ cos x + ∫ 3x² d(sin x)
J = -x³ cos x + 3x² sin x - ∫ 6x sin x dx = -x³ cos x + 3x² sin x + ∫ 6x d(cos x)
J = -x³ cos x + 3x² sin x + 6x cos x - ∫ 6 cos x dx
J = -x³ cos x + 3x² sin x + 6x cos x - 6 sin x + C
7. integral x sin^3 x dx
Penjelasan dengan langkah-langkah:
maaf kalo salah
8. Find the definite integral of ʃπ/20 cos x + sin x dx
Integral~
the definite integral of ʃπ/20 cos x + sin x dx
is
[tex]\boxed{\sf{=\frac{\pi\sin\left(x\right)}{20}-\cos\left(x\right)+C}}[/tex]
[tex] \: [/tex]
Pendahuluan[tex]\boxed{\boxed{\mathbf{A.}} \ \boxed{\mathbf{Pengertian \ Singkat}}}[/tex]
Integral => lawan dari turunan. Jika f(x) turunan pertama dari F(x), maka :
[tex]\boxed{\mathbf{\int_{ }^{ }f\left(x\right)dx=F\left(x\right)+C}}[/tex]
Rumus yang sering dipakai :
[tex]\boxed{\mathbf{\int_{ }^{ }ax^{n}\ dx=\frac{a}{n+1}x^{n+1}+C}}[/tex]
[tex] \: [/tex]
[tex]\boxed{\boxed{\mathbf{B.}} \ \boxed{\mathbf{Integral \ Tak \ Tentu}}}[/tex]
ada 6 integral tak tentu yang perlu anda ketahui, diantaranya :
[tex]\mathbf{1.\ \ \int_{ }^{ }ax^{n}\ dx=\frac{a}{n+1}x^{n+1}+C;n\ne1}[/tex]
[tex]\mathbf{2.\ \ \int_{ }^{ }\frac{1}{x}\ dx=\ln\ | x |+C}[/tex]
[tex]\mathbf{3.\ \ \int_{ }^{ }\sin x\ dx=-\cos x+C}[/tex]
[tex]\mathbf{4.\ \ \int_{ }^{ }\cos x\ dx=\sin x+C}[/tex]
[tex]\mathbf{5.\ \ \int_{ }^{ }e^{x}\ dx=e^{x}+C}[/tex]
[tex]\mathbf{6.\ \ \int_{ }^{ }a^{x}\ dx=\frac{a^{x}}{\ln a}+C}[/tex]
[tex] \: [/tex]
[tex]\boxed{\boxed{\mathbf{C.}} \ \boxed{\mathbf{Integral \ Tentu}}}[/tex]
ada 6 integral tentu juga yang perlu anda pahami, diantaranya :
[tex]\mathbf{1.\ \ \int_{a}^{b}kf\left(x\right)dx=k\int_{a}^{b}f\left(x\right)dx}[/tex]
[tex]\footnotesize\mathbf{2.\ \ \int_{a}^{b}f\left(x\right)\pm g\left(x\right)dx=\int_{a}^{b}f\left(x\right)dx\pm\int_{a}^{b}g\left(x\right)dx}[/tex]
[tex]\mathbf{3.\ \ \int_{a}^{b}f\left(x\right)\ dx=-\int_{b}^{a}f\left(x\right)\ dx}[/tex]
[tex]\small\mathbf{4.\ \ \int_{a}^{b}f\left(x\right)dx+\int_{b}^{c}f\left(x\right)dx=\int_{a}^{c}f\left(x\right)dx}[/tex]
[tex]\mathbf{5.\ \ \int_{a}^{a}f\left(x\right)\ dx=0}[/tex]
[tex]\footnotesize\mathbf{6.\ \ \int_{a}^{b}f\left(x\right)dx=\int_{a+k}^{b+k}f\left(x-k\right)dx=\int_{a-k}^{b-k}f\left(x+k\right)dx}[/tex]
[tex] \: [/tex]
[tex] \: [/tex]
PembahasanDiketahui :
[tex]\large\sf{\int_{ }^{ }(\frac{\pi}{20}\cos (x)+\sin (x)) \ dx}[/tex]
Ditanya :
hasil dari integral tersebut?
Jawaban :
[tex]\large\sf{\int_{ }^{ }(\frac{\pi}{20}\cos (x)+\sin (x)) \ dx}[/tex]
[tex]\large\sf{\frac{\pi}{20}\int_{ }^{ }\cos (x) \ dx +\int_{ }^{ }\sin (x) \ dx }[/tex]
[tex]\large\boxed{\sf{=\frac{\pi\sin\left(x\right)}{20}-\cos\left(x\right)+C}}[/tex]
[tex] \: [/tex]
[tex] \: [/tex]
Pelajari Lebih Lanjut :Contoh soal integral tentu (1) : brainly.co.id/tugas/50510100Contoh soal integral tentu (2) : brainly.co.id/tugas/50454066Tentukan ∫(2x^{2} + 5x)^{2} dx : brainly.co.id/tugas/50364777Integral dari (x^3 +√x) dx : https://brainly.co.id/tugas/50722822[tex] \: [/tex]
[tex] \: [/tex]
Detail Jawaban :Kelas : 12 SMA
Bab : 1
Sub Bab : Bab 1 - Integral
Kode kategorisasi : 12.2.1
Kata Kunci : Integral tak tentu.
9. Integral sin^3 x dx
Itu jawabannya, dicek lg yahInTegraL
∫sin³ x dx
= ∫sin² x . sin x dx
= ∫(1 - cos² x) . d(-cos x)
= -∫dcos x + ∫cos² x dcos x
= -cos x + 1/3 cos³ x + C
10. Integral cos^3 x sin x dx
Integration by Substitution.
∫ cos³ x sin x dx
u = cos x
dx = -du / sin x
= ∫ u³ sin x (-du / sin x)
= -1/4 u⁴ + C
= -1/4 cos⁴ x + C
11. Integral ((4 sin 2x) / ( 3 + sin^2 x))
Gunakan integral substitusi untuk sin²x, atau untuk 3+sin²x. Nanti akan tetap menghasilkan hasil yang sama.
12. integral dari sin x cos^3 x dx
jawab
u = cos x
du = - sin x dx
∫ sin x cos³ dx = - ∫ u³ du = - 1/4 u⁴ + c
= - 1/4 . cos⁴ x + c
13. Integral 3 sin x cos x dx
InTegraL
2 sin x cos x = sin 2x
sin x cos x = 1/2 sin 2x
dcos 2x /dx = -2 sin 2x
sin 2x dx = -1/2 dcos 2x
•••
∫3 sin x cos x dx
= 3/2 ∫ sin 2x dx
= 3/2 ∫ (-1/2) dcos 2x
= -3/4 cos 2x + C
14. integral cos x.3^sin x dx
Jawaban:
liat aja gambarnya
Penjelasan dengan langkah-langkah:
maaf klo slh
15. Integral (x-3) sin x dx
int -(x-3)d(cosx)=
-((x-3)cosx -int cosx d(x-3))
= -((x-3)cosx-sinx))
= sinx -(x-3)cosx
16. subtitusiintegral 3 (x - 9)^9 dxintegral parsialintegral x sin x dx
Jawaban:
Terlampir.
⟡ ⟡ ⟡
[tex]\boxed{\bold{Note\ this:}}[/tex]
◈ Antiderivatif dari fungsi [tex]sin(x)[/tex] adalah [tex]-cos(x)[/tex].
◈ Antiderivatif dari fungsi [tex]cos(x)[/tex] adalah [tex]sin(x)[/tex].
⟡ ⟡ ⟡
[tex]\star\ Semoga\ Membantu\ \star[/tex]
17. integral dari sin x + x pangkat 3 dx adalah
up. pertanyaan yang sama
18. integral (sin x + 3 cos x) dx
= integral sinx +3 integral cosx
= -cosx +3 (sinx)
=3sinx -cosx
#jadikan jawaban tercerdas dan follow sya ya
Penjelasan dengan langkah-langkah:
integral (sin x + 3 cos x) dx
= -cosx+3sinx+c
semogamembantu
19. Integral sin x dx / cos^3 x
Jawab:
Penjelasan dengan langkah-langkah:
[tex]\tt tan\ x = \frac{sin\ x}{cos \ x} \\\tt \int\limits{\frac{sin (x)}{cos^3 (x)} } \, dx = \int\limits{\frac{tan (x)}{cos^2 (x)} } \, dx\\\\= \int\limits {tan \ x \ sec^2 \ x \, dx \\\\= \frac{1}{2} tan^2 \ (x) + c[/tex]
20. Integral dari 3-2 sin x adalah
Materi integral trigonometri
