Evaluate ∫[0 to a] x √(a² - x²) dx. Let substitution t = a² - x².
Evaluate ∫[0 to a] x √(a² - x²) dx. Let substitution t = a² - x².
- A. a²/3
- B. a³/3
- C. 2a³/3
- D. a³/2
Answer: B) a³/3
Explanation: Let t = a² - x², so dt = -2x dx. Limits change from (a² to 0). The integral becomes (1/2) ∫[0 to a²] √t dt = (1/2) [ (2/3) t^(3/2) ] from 0 to a² = 1/3 (a²)^(3/2) = a³/3.
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