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A day full of math games & activities. Find one near you.
How to integrate sin x?
We will use integration by substitution to integrate sin x.
Answer: The final integral of sin x is − cos x + C
Go through the explanation to understand better.
Explanation:
To solve ∫ sin x dx, let sin x = u ⇒ cos x dx = du
By trigonomteric identity: cos2x = 1 - sin2x, we get
⇒ dx = du / cos x = du / √(1 − u2)
∫sin x dx = ∫u (du / √(1 − u2))
= ∫u (1 − u2) -1/2 du
= −1/2 ∫(1−u2)-1/2. (−2u) du
= −1/2 √(1 − u2)/(1/2) + C
= −√(1 − u2) + C
= −√(1 − sin2 x) + C
= −√cos2 x + C
= − cos x + C
Thus, the final integral of sin x is − cos x + C.
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