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Evaluate the definite integral.$\int_{0}^{1}(3 t-1)^{50} d t$
$\frac{1}{153}$
Calculus 1 / AB
Calculus 2 / BC
Chapter 5
Integrals
Section 4
The Substitution Rule
Integration Techniques
Missouri State University
Harvey Mudd College
Baylor University
University of Michigan - Ann Arbor
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Okay, so for this question, we're gonna let you is equal to three t minus one so that 1/3 you is equal to DT, we can change the limits of integration so that what X is equal to one use equal to two on one X is equal to zero. Use equal to negative one, applying a substitution and up with the integral from 0 to 1 of you to the power of 50 times, 1/3 to you. We can fool the 1/3 out. So once we integrate, we end up with that. This is equal to one over 153 and you to the power of 51. And we're gonna do this from 51 0 to 1. And this is just equal to one over 153.
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