R2 = x2 y2 (4) The element of area in polar coordinates is given by rdrdθ, so that the double integral becomes I2 = Z ∞ 0 Z 2π 0 e−r2 rdrdθ (5) Integration over θ gives a factor 2π The integral over r can be done after the substitution u = r2, du = 2rdr Z ∞ 0 e−r2 rdr = 1 2 Z ∞ 0 e−u du = 1 2 (6) 2 Therefore I2 = 2π × 1 2 and Laplace's result (1) is proven A slightlyOrder my "Ultimate Formulmznto/2ZDeifD Hire me for private lessons https//wyzantcom/tutors/jjthetutorRead "The 7 Habits of Successful ST3x 2y = 1 Plot families of exponential and reciprocal graphs For example y = 2 x, y = 3 x, y = 4 x y = 1÷x, y = 2÷x, y = 3÷x, Reduce a given linear equation in two variables to the standard form y = mx c;
Stoke S Theorem Page 2
