Bell-Shaped Curve One of the key results in calculus is the computation of the area
Chapter 15, Problem 57(choose chapter or problem)
Bell-Shaped Curve One of the key results in calculus is the computation of the area under the bell-shaped curve (Figure 24): I = ex2 dx This integral appears throughout engineering, physics, and statistics, and although ex2 does not have an elementary antiderivative, we can compute I using multiple integration. (a) Show that I 2 = J , where J is the improper double integral J = ex2y2 dx dy Hint: Use Fubinis Theorem and ex2y2 = ex2 ey2 . (b) Evaluate J in polar coordinates. (c) Prove that I = .
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