題目 7. (10 points) Compute the following improper integral ∫0∞e−4x2 dx.\int_{0}^{\infty} e^{-4x^2}\,dx.∫0∞e−4x2dx. 解答 解法一 由高斯積分公式， ∫0∞e−4x2 dx=π4.\int_0^\infty e^{-4x^2}\,\mathrm{d}x =\boxed{\frac{\sqrt{\pi}}4}.∫0∞e−4x2dx=4π.
