One of the key results in calculus is the computation of the area under the bellshaped curve (Figure 24):

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This integral appears throughout engineering, physics, and statistics, and although e- does not have an elementary antiderivative, we can compute I using multiple integration. (a) Show that I2 = J, where J is the improper double integral (b) Evaluate J in polar coordinates. (c) Prove that I = . I = 1- Ledx -2 J = Use Fubini's Theorem and e--y=e-e-v. y dx dy N -X