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When we are doing definite integrals, why doesn't the "dummy variable" matter? A dummy variable is a variable we use in a definite integral. We will first see that the dummy variable indeed doesn't matter by using an area argument. Then we will prove that the integral of x^a(1-x)^b from 0 to 1 is the same as the integral of x^b(1-x)^b from 0 to 1 by doing a u-substitution. Hopefully, this video can clear all the questions on the substitution part when we are doing definite integral properties proofs. Get a dx t-shirt 👉 https://bit.ly/dxtee Use "WELCOME10" for 10% off Subscribe for more precalculus & calculus tutorials 👉 #justcalculus ------------------- If you find this channel helpful and want to support it, then you can join the channel membership and have your name in the video descriptions: 👉https://bit.ly/joinjustcalculus buy a math shirt or a hoodie (10% off with the code "WELCOME10"): 👉 https://bit.ly/bprp_merch I use these markers 👉 https://amzn.to/3skwj1E ------------------- 😊 Thanks to all channel members 😊 Seth Morris Andrea Mele John Calculus Maths Class --------------------------------------------------------- "Just Calculus" is dedicated to helping students who are taking precalculus, AP calculus, GCSE, A-Level, year 12 maths, college calculus, or high school calculus. Topics include functions, limits, indeterminate forms, derivatives, and their applications, integration techniques and their applications, separable differential equations, sequences, series convergence tests, power series a lot more. Feel free to leave calculus questions in the comment section and subscribe for future videos 👉 https://bit.ly/just_calc --------------------------------------------------------- Best wishes to you, #justcalculus