integral 4 sin 3x cos 3x dx
1. integral 4 sin 3x cos 3x dx
Misalkan
u= 6x
du/dx= 6
dx= du/6
4 sin3x cos3x -> 2 sin 6x -> 2 sin u
[tex] \int\limits 2 sin u\, du/6[/tex]
-1/3 cos u+c
-1/3 cos 6x+c
2. 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
3. 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.
4. 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
5. 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
6. Integral sin^4(3x)cos^2(3x)dx
Jawaban:
Semoga dapat membantu ya
7. Integral cos^2 3x sin 3x dx =
[tex]\int cos^23xsin3x dx \\\ u=cos 3x \\\ du=-3sin3x~dx \\\ dx= \frac{du}{-3sin3x } \\\ \int u^2sin3x. \frac{du}{-3sin3x} \\\ -\frac{1}{3} \int u^2 \\\ =-\frac{1}{3} \frac{1}{2+1} u^{2+1} +C \\\ =-\frac{1}{3} \frac{1}{3} u^3+C \\\ \boxed{=-\frac{1}{9} cos^33x+C}[/tex]
8. nilai integral dari sin^4 3x cos ^2 3x dx
Jawaban:
=3x^4×3x^2
=3/4+1 x^4+1×3/2+1 x^2+1
=3/5 x^5×3/3x^3
=3/5 x^5 × x^3
=3/5 x^8
maaf klo salah
9. 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
10. Integral sin^4 3x cos^3 3x dx.....
semoga membantu......
11. integral dari 4 sin 5x cos 3x dx
int (4 sin 5x cos 3x) dx
= int (2 . 2 sin 5x cos 3x) dx
= int (2 (sin 8x + sin 2x) dx
= int (2sin8x + 2sin 2x) dx
= -2/8 cos 8x - 2/2 cos 2x + C
= (-1/4) cos 8x - cos 2x + C[tex] \int\limits {4 sin 5x cos 3x} \, dx \\ = \int\limits {4( \frac{1}{2} (sin (5x+3x)+sin(5x-3x) ))} \, dx \\ = \int\limits {2 sin(8x)+sin(2x)}\, dx \\ = \int\limits {2 sin(8x)} \ + \int\limits { sin(2x)} \\ = 2\int\limits {sin(8x)} \ + \int\limits { sin(2x)} \\ =2(- \frac{1}{8} cos8x)+ ( -\frac{1}{2}cos2x) +c\\ =(- \frac{1}{4} cos8x)+ (-\frac{1}{2}cos2x) +c\\ = -\frac{cos8x}{4} -\frac{2cos2x}{4} + c\\ =-\frac{cos8x+2cos2x}{4} + c[/tex]
12. 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
13. integral (sin 3x + 4 cos 2x) dx
semoga membantu yaa ^^
14. integral cos ^5 3x sin 3x dx
dcos 3x = - 3 sin 3x dx
sin 3x dx = -1/3 dcos 3x
∫cos^5 3x . sin 3x dx
= -1/3 ∫cos^5 3x dcos 3x
= -1/3 . 1/6 cos^6 3x + C
= -1/18 cos^6 3x + C
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. Hasil dri Integral sin^4 3x cos 3x dx
penyelesaian terlampir ya.
17. integral 4 sin (3x - 5) cos (3x - 5) dx
sin (3x - 5) cos (3x - 5) = 1/2 ( sin (6x-10) + sin 0) -------> sin 0 = 0
= 1/2.sin(6x-10)
integral 4 sin (3x - 5) cos (3x - 5) dx = int 4.1/2.sin(6x-10) dx
= int 2.sin(6x-10) dx
= 2.1/6.-cos(6x-10) + c
= - 1/3. cos(6x-10) + c
18. integral 4 sin 5x cos 3x dx
kita rubah dulu
4 sin 5x cos 3x=2(2sin 5x cos 3x)
=2(sin (5x+3x)+sin(5x-3x)
=2(sin8x+sin3x)
2sin8x+2sin3x
int4sin5xcos 3x
int(2sin 8x+2sin3x)
int(2sin8x)+int(2sin3x)
2/8cos8x+⅔cos 3x +c
¼ cos 8x +⅔ cos 3x+c
19. integral 4 sin 5x cos 3x dx adalah
int 4 sin(5x) cos(3x) dx
= int 2 (2sin(5x)cos(3x) dx
= 2 int (sin(5x+3x) + sin(5x-3x)) dx
= 2 int (sin(8x) + sin(2x)) dx
= 2 (-1/8 cos(8x) - 1/2 cos(2x)) + C
= -1/4 cos(8x) - cos(2x) + C
20. Integral 4 sin 3x cos x dx
∫ 4 sin 3x cos x dx = 2 ∫ 2 sin 3x cos x dx
= 2∫ sin 4x + sin 2x dx
= 2 { -1/4 cos 4x - 1/2 cos 2x } + c
= -1/2 cos 4x - cos 2x + c
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