Explanation
Step 1: Reason R ki jaanch (f(x) check karein)
Ek function f(x) odd tab hota hai jab f(−x)=−f(x) ho.
Humein diya gaya hai:
Ab x ki jagah −x rakh kar dekhte hain:
Yahan f(−x), na toh f(x) ke barabar hai aur na hi −f(x) ke (kyunki +5 change nahi ho raha).
Iska matlab Reason R galat hai, kyunki x3+5 na toh even function hai aur na hi odd.
Step 2: Assertion A ki jaanch (Integral calculate karein)
Hum integral ko do hisson mein tod sakte hain:
∫−33(x3+5)dx=∫−33x3dx+∫−335dx
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Pehla hissa: x3 ek odd function hai ((−x)3=−x3). Property ke mutabiq, ∫−aa(odd function)dx=0 hota hai.
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Dusra hissa: 5 ek constant (even) function hai.
Toh total value 0+30=30 aayi. Iska matlab Assertion A sahi hai.
Final Answer
Sahi option yeh hoga:
Assertion A is correct, but Reason R is incorrect.
