use-the-technique-of-completing-the-square-to-evaluate-e2x23x1-dxint-inftyinftye

Question

Complete the square to evaluate ∫−∞∞e−(2x2−3x+1) dx\int_{-\infty}^{\infty}$$e^{-(2x^2-3x+1)}$$\,dx given the Gaussian integral formula ∫−∞∞e−ax2dx=πa\int_{-\infty}^{\infty}$$e^{-ax^2}dx$$=\sqrt{\frac{\pi}{a}}.

Accepted Answer

e182π2 \frac{$$e^{\frac18}$$\sqrt{2\pi}}{2}\,

Answer

e18 2π\displaystyle $$e^{\frac18}$$\,\sqrt{2\pi}

Answer

e18 π$$e^{\frac18}$$\,\sqrt{\pi}

Answer

e18π2 \frac{$$e^{\frac18}$$\sqrt{\pi}}{2}\,

Complete the square to evaluate ∫−∞∞e−(2x2−3x+1)dx\(\int\)_{-\(\infty\)}^{\(\infty\)}e^{-(2x^2-3x+1)}\,dx given the Gaussian integral formula ∫−∞∞e−ax2dx=πa\(\int\)_{-\(\infty\)}^{\(\infty\)}e^{-ax^2}dx=\(\sqrt{\frac{\pi}{a}\)}.

Complete the square to evaluate $\int_{- \infty}^{\infty} e^{- (2 x^{2} - 3 x + 1)} d x$ given the Gaussian integral formula $\int_{- \infty}^{\infty} e^{- a x^{2}} d x = \sqrt{\frac{π}{a}}$ .