a surprisingly elegant double integral @drpeyam

Uploaded December 2024 | Updated September 2026, 1 week ago

a surprisingly elegant double integral

We calculate a double integral which looks complicated at first, but becomes much easier in the end. For this, we first convert it to a triple integral and then use a series of u-substitutions and change of variables with Jacobians. Finally, we explore a symmetry in the integral. This is a must-see for multivariable calculus students, enjoy!

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$which logarithm is bigger? The Battle of the Logs. Which is bigger, log base 3 of 5 or log base 5 of 9? The answer may surprise you. We solve this equation by taking the difference, putting on a common denominator, writing it as a single base, and then comparing 3 to the square root of 2 with closer and closer fractions. This logarithmic inequality is applied math and analysis at its finest, and a treat for algebra 2 students and mathematics undergraduates, especially those who like problem solving and logarithmic and exponential equations. YT channel: https://youtube.com/drpeyam TikTok channel: https://www.tiktok.com/@drpeyam Instagram: https://www.instagram.com/peyamstagram/ Twitter: https://twitter.com/drpeyam Teespring merch: https://teespring.com/stores/dr-peyam$