Let I n = x n e -x2 dx, where n is a nonnegative integer. a. I

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Let In = ∫xne-x2 dx, where n is a nonnegative integer. 

a. I0 = ∫ e-x2 dx cannot be expressed in terms of elementary functions. Evaluate I1.    

b. Use integration by parts to evaluate I3.

c. Use integration by parts and the result of part (b) to evaluate I5.

d. Show that, in general, if n is odd, then 4 = * Pa-1(*), u. where pn - 1 is a polynomial of degree n - 1.

e. Argue that if n is even, then In cannot be expressed in terms of elementary functions.

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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