February 25, 2026 A Fun Integral, Part 1 A fun double integral with a nice solution. #math #calculus ProblemEvaluate∫10∫1011−𝑥𝑦d𝑥d𝑦.Solution∫10∫1011−𝑥𝑦d𝑥d𝑦=∫10∫10∑∞𝑘=0(𝑥𝑦)𝑘d𝑥d𝑦=∑∞𝑘=0∫10∫10𝑥𝑘𝑦𝑘d𝑥d𝑦=∑∞𝑘=0(∫10𝑥𝑘d𝑥)(∫10𝑦𝑘d𝑦)=∑∞𝑘=0(1𝑘+1)2=∑∞𝑘=11𝑘2=𝜁(2)=𝜋26. ProblemEvaluate∫10∫1011−𝑥𝑦d𝑥d𝑦.Solution∫10∫1011−𝑥𝑦d𝑥d𝑦=∫10∫10∑∞𝑘=0(𝑥𝑦)𝑘d𝑥d𝑦=∑∞𝑘=0∫10∫10𝑥𝑘𝑦𝑘d𝑥d𝑦=∑∞𝑘=0(∫10𝑥𝑘d𝑥)(∫10𝑦𝑘d𝑦)=∑∞𝑘=0(1𝑘+1)2=∑∞𝑘=11𝑘2=𝜁(2)=𝜋26.