Answer: √π/2.
- A 1
- B π/2
- C √π/2
- D √π
Correct answer: C. √π/2
Explanation: Gaussian integral: let I=∫₀^∞ e<sup>−x²</sup>dx. Then (2I)²=∫∫e<sup>−x²−y²</sup>dx dy over the plane. Converting to polar: 2π∫₀^∞ re<sup>−r²</sup>dr = π. So (2I)²=π, giving I=√π/2.
The exact area under the curve from a to b (shaded) is approximated by a few rectangles, the Riemann sum idea behind the definite integral.