# Answer to Question #4194 in Calculus for John

Question #4194

Prove that integral(bottom=a, top=b) (x

^{2}+1)e^{-x^2}& dx & >= & (e^{-a^2& }- e^{-b^2})Expert's answer

Denote x_1 = 1/2

x_2 = -1/4

x_3 = 1/8

x_4 = -1/16

Then

x

x

x_2 = -1/4

x_3 = 1/8

x_4 = -1/16

Then

x

_{1}= 1/2 = 1/(2^{1}) = (-1)^{1+1}/(2^{1})x_{2}= -1/4 = -1/(2^{2}) = (-1)^{2+1}/(2^{2})x_{3}= 1/8 = 1/(2^{3}) = (-1)^{3+1}/(2^{3})x_{4}= 1/16 = 1/(2^{4}) = (-1)^{4+1}/(2^{4})Thus the general formula for x_n is the followingx

_{n}= -1^{n+1}/ 2^{n}Need a fast expert's response?

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