studymathwithstudent: INTEGRAL FUNGSI TRIGONOMETRI

Rumus Integral Fungsi Trigonometri

1. $\int sin x dx = - cos x + C$

2. $\int cos x dx = sin x + C$

3. $\int tan x dx = - In\left| cos x\right| + C$

4. $\int cot x dx = In\left| sinx\right| + C$

5. $\int sec x dx = In\left| sec x + tan x \right| + C$

6. $\int csc x dx = In \left|cot x - csc x \right| + C$

Contoh Soal Integral Fungsi Trigonometri

1. $\int (4 sin x + cos x)dx =$

Jawaban:

$\int (4 sin x + cos x)dx = -4 cos x + sin x + C$

2. $\int cos (x) - sec (x)dx =$

Jawaban:

$\int cos (x) - sec (x)dx = \int cos (x) dx - \int sec (x) dx$

$\int cos (x) dx - \int sec (x) dx = sin (x) - In\left| tan (x) + sec (x)\right| + C$

3. $\int (sin (3x) - cos (3x)) ^{2} dx =$

Jawaban:

$\int (sin (3x) - cos (3x)) ^{2} dx = \int (sin^{2}3x + cos^{2}3x - 2sin 3x.cos 3x) dx$

$\int (sin (3x) - cos (3x)) ^{2} dx = \int (1 - sin 2.3x) dx$

$\int (sin (3x) - cos (3x)) ^{2} dx = \int (1 - sin 6x) dx$

$\int (sin (3x) - cos (3x))^{2} dx = x - (-\frac{1}{6} cos (6x))+ C$

$\int (sin (3x) - cos (3x))^{2} dx = x + \frac{1}{6} cos (6x) + C$

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