- #1
Jamin2112
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Homework Statement
1) What is a cool way to prove that ∫e-x2dx = √π / 2 ?
2) What does it mean if ∫f(x,t)dt converges uniformly on the interval a ≤ x ≤b? Does it basically mean that it'll converge for all x in that interval? Explain this to me as if I were an 8-year-old girl.
3) My book uses a variation of Dirichlet's Test to show that ∫sin(x) / x is convergent (bounds: 0, ∞). But if we use ø(x) = 1/x, like the book does, then isn't ø'(x) = -1/x2 not continuous? The book doesn't say anything about this.
Homework Equations
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The Attempt at a Solution
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