integral dari cos 3x cos x dx=.... integral dari cos² 4x dx=...
1. integral dari cos 3x cos x dx=.... integral dari cos² 4x dx=...
semoga membantu yaa.. ^_^
2. Hasil dari pengintegralan berikut adalah.. integral dari (cos 3x cos 2x - sin 3x sin 2x)dx
ingat ubah dulu kedalam rumus jumlah trigonometri
int (( 1/2 cos 5x + 1/2 cos x ) - (- ( 1/2 cos 5x + 1/2 cos x )) dx
1/10 sin 5x + 1/2 sin x + 1/10 sin 5x + 1/2 sin x + c
3. integral cos 3x cos x dx = ....?
∫ cos(3x)cosx dx
= ∫(1/2)(cos(3x + x) + cos(3x - x)) dx
= ∫(1/2)(cos(4x) + cos(2x)) dx
= (1/2)∫cos(4x) + cos(2x) dx
= (1/2)(1/4)sin(4x) + (1/2)(1/2)sin(2x) + C
= (1/8)sin(4x) + (1/4)sin(2x) + C
4. tentukan hasil integral dari trigonometri berikut : 1. integral sin (4x - 2 ) dx 2. integral 6 cos 4x dx 3. integral (5 sin x - cos (4 - 3x)) dx 4. integral (cos 3x - 2 sin 2x ) dx 5. integral 15 sin 2x cos 3x dx 6. integral cos 4x cos 2x dx 7. integral (sin 7x cos 3x ) dx
Kalo kurang jelas tanya aja. Semoga membantu.
5. Integral cos (3x-5) dx
int cos (3x - 5) dx = (1/3) sin (3x - 5) + c
6. tentukan hasil integral dari trigonometri berikut : 1. integral sin (4x - 2 ) dx 2. integral 6 cos 4x dx 3. integral (5 sin x - cos (4 - 3x)) dx 4. integral (cos 3x - 2 sin 2x ) dx 5. integral 15 sin 2x cos 3x dx 6. integral cos 4x cos 2x dx 7. integral (sin 7x cos 3x ) dx
nomer 1
integral sin (4x - 2 ) dx
= -1/4.cos (4x - 2) + C
nomer 2
integral 6 cos 4x dx
= -3/2.sin 4x + C
nomer 3
integral (5 sin x - cos (4 - 3x)) dx
= -5.cos x + 1/3.sin (4 - 3x) + C
nomer 4
integral (cos 3x - 2 sin 2x ) dx
= 1/3.sin 3x + cos 2x + C
nomer 5
integral 15 sin 2x cos 3x dx
= integral 15/2.(2. sin 2x cos 3x) dx
= integral 15/2.(sin (5/2)x + sin (-1/2)x) dx
= integral 15/2.sin (5/2)x + 15/2.sin (-1/2)x) dx
= -3.cos (5/2)x +15.cos (1/2)x + C
nomer 6
integral cos 4x cos 2x dx
= integral 1/2.(2.cos 3x + 2.cos x)dx
= integral (cos 3x + cos x)dx
= 1/3.sin 3x + sin x + C
nomer 7
integral (sin 7x cos 3x ) dx
= integral 1/2.(2.sin 7x cos 3x ) dx
= integral 1/2.(sin 5x + sin 2x) dx
= integral (1/2.sin 5x + 1/2.sin 2x) dx
= -1/10.cos 5x -1/4.cos 2x + C
7. integral 2sin5x cos 3x dx
ini jawabannya ya!!
TOLONG JADIIN JAWABAN TERBAIK YAAA
8. integral cos² 3x. dx =
∫cos 3x cos 3x dx
= 1/2 ∫ cos 6x + cos 0 dx
= 1/2 ∫ cos 6x + 1 dx
= 1/2 (1/6 sin 6x + x + c
= 1/12 sin 6x + 1/2 x + c
9. integral cos 3x dx caranya
cos 3x dx= 1/3 sin 3x+c
10. integral 2 cos 5x cos 3x
Int (2 cos 5x cos 3x) dx
= Int (cos (5x+3x) + cos (5x-3x)) dx
= Int (cos 8x + cos 2x) dx
= 1/8 sin 8x + 1/2 sin 2x + C
11. 1. integral 1 / cos^6(3x + 2) = ?2. integral cos^2 3x dx = ?3. integral sin^2 dx = ?
1) int 1/cos^6 (3x+2) dx
= int sec^6 (3x+2) dx
misal :
u = 3x + 2
du = 3 dx ----> dx = 1/3 du
so,
=1/3 int sec^6 (u) du
= 1/3 int (sec^2(u))^2 sec^2(u) du
= 1/3 int (1+tan^2(u))^2 sec^2(u) du
= 1/3 int (1 + 2 tan^2(u) + tan^4(u)) sec^2u) du
split menjadi 3 integral :
= 1/3 int sec^2(u) du + 2/3 int tan^2(u) sec^2(u) du + 1/3 int tan^4(u) sec^2(u) du
jelas, untuk 1/3 int sec^2(u) du = 1/3 tan(u)
untuk yg lainnya gunakan int u-subs,
misal y = tan(u)
dy = sec^2(u) du
shg, diperoleh :
2/3 int tan^2(u)sec^2(u)du + 1/3 int tan^4(u)sec^2(u) du
= 2/3 int y^2 dy + 1/3 y^4 dy
= 2/3 * 1/3 y^3 + 1/3 * 1/5 y^5 + C
= 2/9 y^3 + 1/15 y^5 + c
substitusikan kembali bahwa y = tan(u), maka
= 2/9 tan^3 (u) + 1/15 tan^5 (u)
shg totalnya,
1/3 tan(u) + 2/9 tan^3 (u) + 1/15 tan^5 (u) + C
finally, substitusikan kembali u = (3x + 2)
so,
= 1/3 tan(3x+2) + 2/9 tan^3 (3x+2) + 1/15 tan^5 (3x+2) + C
2) int cos^2 (3x) dx
= int (1 + cos(6x))/2 dx
= int 1/2 dx + 1/2 cos(6x) dx
= 1/2 x + 1/12 sin(6x) + C
3) int sin^2 apa ya .... hehe, i was tired :)
12. integral 4 cos 2x cos 3x dx
ingat dengan 2 cos A cos B = cos (A+B) + cos (A-B)
∫ 4 cos 3x cos 2x dx = 2 ∫ 2 cos 3x cos 2x dx
= 2 ∫cos 5x + cos x dx
= 2 { 1/5 sin 5x + sin x)
= 2/5 sin 5x + sin x
= 2/5 ( sin x + 5 sin x) +C
13. Integral 2 cos 3x cos x
int2cos3xcosx
=int(cos4x + cos2x)
=1/4 sin4x + 1/2 sin2x + C
14. integral tak tentu cos 3x cos x dx
ini jawaban q, klo salah maapin :)
15. 1 a. Integral sin x . cos x dx b. Integral sin 3x . cos 3x dx c. Integral sin²x dx 2 a. Integral 2 sin 4x . cos 2x dx b. Integral cos 6x . sin 3x dx c. Integral cos 4x . cos 6x dx d. Integral sin 2x . sin x dx
InTegraL
∫sn x cos x dx
= 1/2 ∫sin 2x dx
= -1/4 ∫dcos 2x
= -1/4 cos 2x + C
∫sin 3x cos 3x dx
= 1/2 ∫sin 6x dx
= -1/12 ∫dcos 6x
= -1/12 cos 6x + C
∫cos 6x sin 3x dx
= 1/2 ∫(sin 9x - sin 3x) dx
= -1/18 cos 9x + 1/6 cos 3x + C
16. integral ∫ 12x²cos(3x)
Jawaban:
(-36x²+648)sin3x+216 x cos 3x + C
Penjelasan dengan langkah-langkah:
penyelesaian ada pada gambar
semoga membantu
17. tentukan integral tentu/tak tentu dari : a. integral cos (3x+2) dxb. integral 1 integral 0 (3x+2)³ dx
Jawaban:
a. integral cos 3x-2 dx
= 1/3sinx-2x +c
b. int (3x - 2)³ dx
= ⅓ • ¼ (3x - 2)⁴ + C
= 1/12 (3x - 2)⁴ + C
Penjelasan dengan langkah-langkah:
semoga membantu
18. integral cos² 3x. dx =
[tex] \int cos^2{3x} \, dx =\int(\frac{1}{2}+\frac{cos6x}{2})\ dx\\ \\ \int cos^2{3x} \, dx =\int\frac{1}{2}\ dx+\int\frac{cos6x}{2}\ dx\\ \\ \int cos^2{3x} \, dx =\frac{1}{2}x+\frac{sin6x}{12}+C[/tex]
19. integral (cos x+cos^3x+cos^5x+.....) dx
cos x + (cos x)^3 + (cos x)^5 + ...
S~ = a/(1 - r)
S~ = cos x/(1 - cos² x)
S~ = cos x / sin² x
S~ = csc x cot x
∫(cos x + (cos x)^3 + (cos x)^5 + ... ) dx
= ∫csc x cot x dx
= - ∫dcsc x
= - csc x + c
20. integral dari sin 3x cos 3x dx adalah
Integral Trigo
∫ sin 3x cos 3x dx =
= ∫ 1/2 (2 sin 3x cos x ) dx
= ∫ 1/2 (sin 6x) dx
= 1/2 . 1/6 . (- cos 6x) + c
= - 1/12 cos 6x + c
21. integral (3x+1) cos 3x dx
∫(3x+1)cos3x dx = ∫ 3x cos3x + cos3x dx
∫ 3x cos3x dx = ∫ udv
u = 3x, du = 3 dx
dv=cos3x dx, v = (1/3)sin3x
∫ 3x cos3x dx = ∫ udv = vu-∫ vdu
= (3x)(1/3)sin3x- ∫ (1/3) sin3x (3) dx
=sin3x- ∫ sin3x dx
=-x sin3x + (1/3) cos3x + C
∫(3x+1)cos3x dx = ∫ 3x cos3x dx + ∫ cos3x dx
=(x sin3x + (1/3) cos3x + C ) + (1/3) sin3x
=(1/3)((3x+1) sin3x+cosx)) + C
Komentar · tidak puas? sampaik
22. integral dari 6 cos 3x cos x adalah. . .
∫ 6 cos 3x cos dx = 3∫ 2 cos 3x cos x dx
= 3 ∫cos (3x+x) + cos (3x-x) dx
= 3 ∫ cos 4x + cos 2x
= 3 (-1/4 sin 4x + 1/2 sin 2x) +c
= -3/4 sin 4x + 3/2 sin 2x + c
= -3/4 ( sin 4x - 2 sin 2x ) + C
23. hasil dari integral 16 cos 7x cos 3x adalah...
ini jawabannya. saya menulis ini untuk memenuhi menjawab minimal 20 karakter. semoga membantu :D
24. Integral 10 cos 3x cos 2x dx
semoga membantu yaa :)InTegraL FunGsi TrigOnoMetRi
2 cos 3x cos 2x = cos 5x + cos x
∫10 cos 3x cos 2x dx
= 5 ∫2 cos 3x cos 2x dx
= 5 ∫(cos 5x + cos x) dx
= 5 ( 1/5 ∫dsin 5x + ∫dsin x)
= 5 (1/5 sin 5x + sin x) + C
= sin 5x + 5 sin x + C
25. Berapakah nilai Integral berikut A). Integral sin 3x sin xdx B). Integral cos 8x cos 6xdx
Integral Trigonometri
ubah rumus perkalian ke rumus jumlah
A) sin 3x sin x = -1/2 ( -2 sin 3x sin x)
sin 3x sin x = - 1/2 { cos(3x + x) - cos (3x -x)}
sin 3x sin x = -1/2 { cos 4x - cos 2x }
∫ sin 3x sin x dx = - 1/2 ∫ cos 4x - cos 2x dx
= - 1/2 { 1/4 sin 4x - 1/2 sin 2x } + c
= -1/8 sin 4x + 1/4 sin 2x + c
B) cos 8x cos 6x = 1/2 { 2 cos 8x cos 6x )
= 1/2 { cos (8x+6x) + cos(8x-6x)}
= 1/2 { cos 14x + cos 2x }
∫ cos 8x cos 6x dx = 1/2 ∫ cos 14 x + cos 2x dx
= 1/2 { 1/14 sin 14x + 1/2 sin 2x } + c
= 1/28 sin 14 x + 1/4 sin 2x + c
26. integral 8 cos 3x cos 2x dx
jawabannya
4/3 sin 3x sin 2x
27. integral dari 3 cos 3x cos x
InTegraL
cos 3x cos x
= 1/2 (cos (3x+x) + cos (3x-x))
= 1/2 (cos 4x + cos 2x)
∫3 cos 3x cos x dx
= 3 . 1/2 ∫(cos 4x + cos 2x) dx
= 3/2 (1/4 ∫dsin 4x + 1/2 ∫dsin 2x)
= 3/8 sin 4x + 3/4 sin 2x + C ✔
28. integral cos x cos 3x DX
Sin x Sin 3x
maaf kalau salah
29. Berapa hasil integral cos 3x cos 7x dx?
integral cos 3x cos 7x dx= 1/2 int (cos 4x+cos 10x) dx
=1/8 sin 4x +1/20 sin 10 x + c
30. nilai dari integral cos 5x cos 3x adalah
∫cos 5x cos 3x
∫1/2 (cos (5x + 3x) +(cos (5x-3x)
∫1/2 (cos 8x ) + (cos 2x)
1/2 (1/8 sin 8x + 1/2 sin 2x) +c
1/16 sin 8x + 1/4 sin 2x + c
1/16 sin 8x + 1/4 sin 2x
31. integral 16 cos 7x cos 3x dx
∫16 cos 7x cos 3x dx=...?
ingat! 2 cos α.cos β= cos (α+β) + cos (α-β)
⇒Jawab
= 16 ∫ cos 7x cos 3x dx
= 16/2 ∫ 2 cos (7x+3x) + cos (7x-3x) dx
= 16/2 ∫ cos 10x + cos 4x dx
= 16/2 (sin 10x + sin 4x) + C
= 16/20 sin 10x + 16/8 sin 4x + C
= 4/5 sin 10x + 2 sin 4x + C
32. integral cos² 3x dx
Jawaban:
tengyu ...............
33. integral cos kuadrat 3x sin 3x
integral cos^2 3x sin 3x = -3/2 sin 3x 1/3 cos 3x
34. integral 6 cos 3x cos 6 dx
jadikan jawaban terbaik jika membantu ya :)
35. Integral cos 7x cos 3x dx
Dengan:
cos A cos B = 1/2 (cos(A+B) + cos(A-B))
Maka:
[tex]$\begin{align}\int\cos7x\cos3x\, dx&=\int\frac12(\cos(7x+3x)+\cos(7x-3x))\, dx \\ &=\frac12\int\cos10x+\cos4x\, dx \\ &=\frac12\left[\frac1{10}\sin10x+\frac14\sin4x\right]+C \\ &=\frac1{40}(2\sin10x+5\sin4x)+C\end{align}[/tex]
int cos7x cos3x dx
= int 1/2 (cos(7x+ 3x) + cos(7x-3x)) dx
= 1/2 int (cos10x + cos4x) dx
= 1/2(1/10 sin10x + 1/4 sin4x) dx
= 1/20 sin10x + 1/8 sin4x + c
36. Integral (cos^3x) dx?
semoga bermanfaat yaa~♡
37. Integral cos 4x cos 3x dx
∫ cos 4x.cos 3x dx
= ∫1/2(cos 7x + cos x) dx
= 1/2(1/7.sin 7x + sin x) + C
= 1/14.sin 7x + 1/2.sin x + C
38. Integral cos 5x cos 3x dx
Dengan aturan penjumlahan dan selisih sudut, akan diperoleh:
cos A . cos B = 1/2 (cos(A+B) + cos(A-B))
Sehingga:
cos 5x . cos 3x
= 1/2 [cos(5x+3x) + cos(5x-3x)]
= 1/2 [cos 8x + cos 2x]
Dengan integralnya adalah:
∫ cos 5x.cos 3x dx
= ∫ 1/2 (cos 8x + cos 2x) dx
= 1/2 ∫ (cos 8x + cos 2x) dx
Mengingat:
∫ cos ax dx = 1/a sin ax + C
Menghasilkan:
= 1/2 (1/8 sin 8x + 1/2 sin 2x) + C
= 1/16 sin 8x + 1/4 sin 2x + C
39. integral cos kuadrat 3x dx =
-3² sin 3x = 6 sin 3x
40. Integral (cos 3x cos x - sin 3x sin x) dx=
∫(cos 3x cos x - sin 3x sin x) dx = ∫ cos 4x dx
= (1/4).sin 4x + C
