Using the formula 4 × ∫(0 to r) √(r² − x²) dx for the area of a circle, what is the exact evaluated value of the integral ∫(0 to r) √(r² − x²) dx?
Using the formula 4 × ∫(0 to r) √(r² − x²) dx for the area of a circle, what is the exact evaluated value of the integral ∫(0 to r) √(r² − x²) dx?
- A. πr²/4
- B. πr²
- C. πr²/2
- D. r²/2
Answer: A) πr²/4
Explanation: Since the total area is πr² and the formula multiplies the integral by 4, the integral itself (representing one quadrant) must evaluate to πr²/4.
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