∫√(a² − x²) dx (with a > 0) equals:
∫√(a² − x²) dx (with a > 0) equals:
- A. (x/2)√(a²−x²) + (a²/2)sin⁻¹(x/a) + C
- B. x√(a²−x²) + sin⁻¹(x/a) + C
- C. (1/2)√(a²−x²) + C
- D. a²sin⁻¹(x/a) + C
Answer: A) (x/2)√(a²−x²) + (a²/2)sin⁻¹(x/a) + C
Explanation: Standard formula: ∫√(a²−x²) dx = (x/2)√(a²−x²) + (a²/2)sin⁻¹(x/a) + C. Can be derived by substituting x = a sin θ.
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