E-PI03 · Choose the antiderivative coefficient
For \(\displaystyle x>\frac13\), define \(\displaystyle F_{a}(x)= a(3x- 1)^{\frac{5}{2}}\).
Find \(F_a^{\prime}(x)\).
Find a so that \(F_a\) is an antiderivative of \(\displaystyle 6(3x- 1)^{\frac{3}{2}}\). Give the general indefinite integral.
Evaluate \(\displaystyle \int_{\frac{1}{3}}^{\frac{5}{3}} 6(3x- 1)^{\frac{3}{2}}\, dx\). Explain why the lower endpoint is permitted.
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