Integral Trigonometri
∫ sin x dx = - cos x + C
∫ cos x dx = sin x + C
∫ sec² x dx = tan x + C
∫ cosec² x dx = - cot x + C
∫ sec x tan x dx = sec x + C
∫ cosec x cot x dx = - cosec x + C
Identitas Trigonometri
sin² x + cos² x = 1
tan² x + 1 = sec² x
cot² x + 1 = cosec² x
=
= tan x - cot x
= (tan π - cot π) - (tan 0 - cot 0)
= (0 - cot π) - (0 - cot 0)
= - cot π + cot 0
= 0
karena cot π = cot 0
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Verified answer
Integral Trigonometri
∫ sin x dx = - cos x + C
∫ cos x dx = sin x + C
∫ sec² x dx = tan x + C
∫ cosec² x dx = - cot x + C
∫ sec x tan x dx = sec x + C
∫ cosec x cot x dx = - cosec x + C
Identitas Trigonometri
sin² x + cos² x = 1
tan² x + 1 = sec² x
cot² x + 1 = cosec² x
=![\mathop{\int}\limits_{0}\limits^{\pi}{(tan \: x + \frac{1}{tan \: x})^{2}} \: dx \mathop{\int}\limits_{0}\limits^{\pi}{(tan \: x + \frac{1}{tan \: x})^{2}} \: dx](https://tex.z-dn.net/?f=%5Cmathop%7B%5Cint%7D%5Climits_%7B0%7D%5Climits%5E%7B%5Cpi%7D%7B%28tan%20%5C%3A%20x%20%2B%20%5Cfrac%7B1%7D%7Btan%20%5C%3A%20x%7D%29%5E%7B2%7D%7D%20%5C%3A%20dx)
=![\mathop{\int}\limits_{0}\limits^{\pi}{tan^{2} \: x + 2 \: . \: tan \: x \: . \: \frac{1}{tan \: x} + \frac{1}{tan^{2} \: x}} \: dx \mathop{\int}\limits_{0}\limits^{\pi}{tan^{2} \: x + 2 \: . \: tan \: x \: . \: \frac{1}{tan \: x} + \frac{1}{tan^{2} \: x}} \: dx](https://tex.z-dn.net/?f=%5Cmathop%7B%5Cint%7D%5Climits_%7B0%7D%5Climits%5E%7B%5Cpi%7D%7Btan%5E%7B2%7D%20%5C%3A%20x%20%2B%202%20%5C%3A%20.%20%5C%3A%20tan%20%5C%3A%20x%20%5C%3A%20.%20%5C%3A%20%5Cfrac%7B1%7D%7Btan%20%5C%3A%20x%7D%20%2B%20%5Cfrac%7B1%7D%7Btan%5E%7B2%7D%20%5C%3A%20x%7D%7D%20%5C%3A%20dx)
=![\mathop{\int}\limits_{0}\limits^{\pi}{tan^{2} \: x + 2 + cot^{2} \: x} \: dx \mathop{\int}\limits_{0}\limits^{\pi}{tan^{2} \: x + 2 + cot^{2} \: x} \: dx](https://tex.z-dn.net/?f=%5Cmathop%7B%5Cint%7D%5Climits_%7B0%7D%5Climits%5E%7B%5Cpi%7D%7Btan%5E%7B2%7D%20%5C%3A%20x%20%2B%202%20%2B%20cot%5E%7B2%7D%20%5C%3A%20x%7D%20%5C%3A%20dx)
=![\mathop{\int}\limits_{0}\limits^{\pi}{(sec^{2} \: x - 1) + 2 + (cosec^{2} \: x - 1)} \: dx \mathop{\int}\limits_{0}\limits^{\pi}{(sec^{2} \: x - 1) + 2 + (cosec^{2} \: x - 1)} \: dx](https://tex.z-dn.net/?f=%5Cmathop%7B%5Cint%7D%5Climits_%7B0%7D%5Climits%5E%7B%5Cpi%7D%7B%28sec%5E%7B2%7D%20%5C%3A%20x%20-%201%29%20%2B%202%20%2B%20%28cosec%5E%7B2%7D%20%5C%3A%20x%20-%201%29%7D%20%5C%3A%20dx)
=![\mathop{\int}\limits_{0}\limits^{\pi}{sec^{2} \: x + cosec^{2} \: x } \: dx \mathop{\int}\limits_{0}\limits^{\pi}{sec^{2} \: x + cosec^{2} \: x } \: dx](https://tex.z-dn.net/?f=%5Cmathop%7B%5Cint%7D%5Climits_%7B0%7D%5Climits%5E%7B%5Cpi%7D%7Bsec%5E%7B2%7D%20%5C%3A%20x%20%2B%20cosec%5E%7B2%7D%20%5C%3A%20x%20%7D%20%5C%3A%20dx)
= tan x - cot x![_{0}I^{\pi} _{0}I^{\pi}](https://tex.z-dn.net/?f=_%7B0%7DI%5E%7B%5Cpi%7D)
= (tan π - cot π) - (tan 0 - cot 0)
= (0 - cot π) - (0 - cot 0)
= - cot π + cot 0
= 0
karena cot π = cot 0