First Notebook

A Study of Improper Integrals

Math. 487-01, Spring, 2004
R. Baker Kearfott

(∫_0^1) 1/x \[DifferentialD]x

NIntegrate[1/x, {x, 0, 1}]

(∫_0^1) 1/(Sqrt[x]) \[DifferentialD]x

NIntegrate[1/(Sqrt[x]), {x, 0, 1}]

(∫_0^1) 1.0/(Sqrt[x]) \[DifferentialD]x

Limit[(∫_ϵ^1) 
            1/(Sqrt[x]) \[DifferentialD]x, ϵ ->  0]

Limit[ArcTan[x], x -> ∞]

(∫_1^∞) 1/x^2 \[DifferentialD]x

NIntegrate[1/x^2, {x, 1, ∞}]

(∫_0^π) Sin[x]/x \[DifferentialD]x

NIntegrate[Sin[x]/x, {x, 0, π}]

N[(∫_0^π) Sin[x]/x \[DifferentialD]x, 20]

Working with series

Next time: Taylor approximations to the above integrals