Converging Improper Integrals...Good Luck :)

Level 2

For what pairs ( a , b ) (a,b) of positive real numbers does the improper integral

∫ b ∞ ( x + a − x − x − x − b ) d x \displaystyle \int_b^{\infty}(\sqrt{\sqrt{x+a}-\sqrt{x}}-\sqrt{\sqrt{x}-\sqrt{x-b}})dx

converge?

a < b a<b a > b a>b The integral doesn't converge. a = b a=b

Vishruth Bharath by Vishruth Bharath , 17, USA

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