Uploaded April 2022 | Updated September 2026, 1 week ago
Calculating integral using Laplace transforms. Evaluating integral of x^m (1-x)^n from 0 to 1 using convolution and Laplace transforms of functions, which is useful for engineering systems. I use a u sub and then apply the transform to power functions, which then turns it into a product of transforms. This is much faster and elegant than expanding and using the binomial theorem. There will be factorials involved and I also mention an extension to gamma functions. This is a must-see for calculus students, engineers, mathematicians, and differential equations lovers.
0:00 Introduction
0:50 Convolution
4:00 Laplace transform
6:07 The answer
Convolution Intuition: youtu.be/_8LwWEGNyyM
YT channel: youtube.com/drpeyam
TikTok channel: tiktok.com/@drpeyam
Instagram: instagram.com/peyamstagram
Twitter: twitter.com/drpeyam
Teespring merch: teespring.com/stores/dr-peyam
Calculating integral using Laplace transforms. Evaluating integral of x^m (1-x)^n from 0 to 1 using convolution and Laplace transforms of functions, which is useful for engineering systems. I use a u sub and then apply the transform to power functions, which then turns it into a product of transforms. This is much faster and elegant than expanding and using the binomial theorem. There will be factorials involved and I also mention an extension to gamma functions. This is a must-see for calculus students, engineers, mathematicians, and differential equations lovers.
0:00 Introduction
0:50 Convolution
4:00 Laplace transform
6:07 The answer
Convolution Intuition: youtu.be/_8LwWEGNyyM
YT channel: youtube.com/drpeyam
TikTok channel: tiktok.com/@drpeyam
Instagram: instagram.com/peyamstagram
Twitter: twitter.com/drpeyam
Teespring merch: teespring.com/stores/dr-peyam
