7. [-/1 Points] DETAILS SCALC9 4.5.038.
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Evaluate the definite integral.
\[
\int_{0}^{3}(3 t-1)^{60} d t
\]
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Answer
Final Answer: The definite integral of the function \((3t-1)^{60}\) from 0 to 3 is approximately \(\boxed{6.69943405843012 \times 10^{52}}\).
Step 1 ：Given the integral \(\int_{0}^{3}(3 t-1)^{60} d t\)
Step 2 ：Let's try the substitution u = 3t - 1. Then du = 3dt, or dt = du/3. The limits of integration also change: when t = 0, u = -1, and when t = 3, u = 8.
Step 3 ：The integral then becomes \((1/3)\int_{-1}^{8} u^{60} du\), which can be solved using the power rule.
Step 4 ：The result of the integral calculation is a very large number, approximately 6.69943405843012E+52.
Step 5 ：Final Answer: The definite integral of the function \((3t-1)^{60}\) from 0 to 3 is approximately \(\boxed{6.69943405843012 \times 10^{52}}\).
