Answer to Question #4194 in Calculus for John

Question #4194
Prove that integral(bottom=a, top=b) (x[sup]2[/sup]+1)e[sup]-x^2[/sup]& dx & >= & (e[sup]-a^2& [/sup]- e[sup]-b^2[/sup])
Expert's answer
Denote x_1 = 1/2
x_2 = -1/4
x_3 = 1/8
x_4 = -1/16
Then
x1 = 1/2 = 1/(21) = (-1)1+1/(21)x2 = -1/4 = -1/(22) = (-1)2+1/(22)x3 = 1/8 = 1/(23) = (-1)3+1/(23)x4 = 1/16 = 1/(24) = (-1)4+1/(24)Thus the general formula for x_n is the following
xn = -1n+1/ 2n

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