CONTOH SOAL INTEGRAL FUNGSI TRIGONOMETRI

Contoh Soal Integral Fungsi Trigonometri

Contoh 1
∫ sin²x dx = ...

Jawab :⇒∫ (12−1212−12cos 2x) dx
= 1212x − 1212. 1212sin 2x + C
= 1212x − 1414sin 2x + C


Contoh 2
∫ (sin 3x − cos 3x)² dx = ...

Jawab :⇒∫ (sin²3x + cos²3x − 2 sin 3x cos 3x) dx
⇒∫ (1 − sin 2.3x) dx
⇒∫ (1 − sin 6x) dx
= x − (−16−16cos 6x) + C
= x + 1616cos 6x + C


Contoh 3
 ∫ (tan²4x + 3) dx = ...

Jawab :⇒∫ (sec²4x − 1 + 3) dx
⇒∫ (sec²4x + 2) dx
= 1414tan 4x + 2x + C


Contoh 4
∫ (tan 2x − sec 2x)² dx = ...

Jawab :⇒∫ (tan²2x + sec²2x − 2 sec 2x tan 2x) dx
⇒∫ (sec²2x − 1 + sec²2x − 2 sec 2x tan 2x) dx
⇒∫ (2sec²2x − 2 sec 2x tan 2x − 1) dx
= 2222tan 2x − 2222sec 2x − x + C
= tan 2x − sec 2x − x + C


Contoh 5
∫ 4 sin 4x cos 2x dx = ...

Jawab :⇒∫ 4242[sin (4x+2x) + sin (4x−2x)] dx
⇒∫ (2sin 6x + 2sin 2x) dx
= −26−26cos 6x + (−22−22cos 2x) + C
= −13−13cos 6x − cos 2x + C


Contoh 6
∫1−tan2xsec2x∫1−tan2xsec2x dx = ...

Jawab :⇒∫ 1−(sec2x−1)sec2x1−(sec2x−1)sec2x dx
⇒∫ 2−sec2xsec2x2−sec2xsec2x dx
⇒∫ (2sec2x−sec2xsec2x)(2sec2x−sec2xsec2x) dx
⇒∫ (2cos²x − 1) dx
⇒∫ cos 2x dx
= 1212sin 2x + C