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Problem 54 Hard Difficulty

Evaluate the definite integral.

$ \displaystyle \int^1_0 (3t - 1)^{50} \, dt $

Answer

$\frac{2^{51}+1}{153} \approx 1.47 \times 10^{13}$

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Video Transcript

okay for this problem. The first thing we know is that you is three t minus one, which means that 1/3 times do you were transferring this three over here, so it becomes 1/3. There's a quote. Want to DT? It's now Our original function can now be written with our constant 1/3 on the outside and then you to the 50th. Do you using the power rule increased the exploited by 1 to 51. Divide by the new exponents.