integration of trigonometric functions
Understand the Problem
Ye prashna trigonometric functions ke integration ke baare mein hai, jismein humein yeh samajhna hai ki kaise in functions ka integration kiya jata hai.
Answer
$$ \int sin(x) \, dx = -cos(x) + C $$
Answer for screen readers
$$ \int sin(x) , dx = -cos(x) + C $$
Steps to Solve
- Identify the Trigonometric Function
Pehle humein is prashna mein diye gaye trigonometric function ko pehchan na hoga. Maan lo ke humare paas $sin(x)$ ka integration hai.
- Write the Integral
Ab humein integral likhna hai. Agar hum $sin(x)$ ka integral le rahe hain, toh yeh hoga:
$$ \int sin(x) , dx $$
- Apply the Integration Rule
$sin(x)$ ka integration karne ke liye humein yeh rule yaad rakhna hoga:
$$ \int sin(x) , dx = -cos(x) + C $$
yahan $C$ integration constant hai.
- Write the Final Result
Ab hum apne solved result ko likhte hain:
$$ \int sin(x) , dx = -cos(x) + C $$
$$ \int sin(x) , dx = -cos(x) + C $$
More Information
Is jawab ka matlab hai ke $sin(x)$ ka integration karte samay aapko $-cos(x)$ milega. Yeh integration constant $C$ uss situation ko darshata hai jab kisi specific limit ka zikar nahi hota.
Tips
- Kabhi-kabhi log integration ke process mein sign bhool jaate hain. Jaise ki, $sin(x)$ ka integration $-cos(x)$ hai, jo kayi baar confuse kar sakta hai.
- Kuch log integration constant $C$ ko nahi likhte, jo galat hota hai kyunki jab bhi hum indefinite integral lete hain, hamesha $C$ add karna chahiye.
