The mathematical glow-up nobody asked for but everyone needed! Regular definite integrals are just hanging out in their pajamas, but throw a limit as t approaches infinity on that bad boy and suddenly it's wearing a tuxedo to the calculus ball. It's like watching your sloppy integral clean up for a fancy mathematical soirée. Even Winnie the Pooh knows that improper integrals just hit different - they're the same calculation underneath but with that extra touch of sophistication that makes calculus professors weak at the knees.
Looking Proper With Improper Integrals

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