Problem
Using the substitution $u=5 x-2$, the integral below can be transformed into a simpler integral:
\[
\int_{0}^{1}(5 x-2)^{2 / 3} d x=\int_{a}^{b} c u^{2 / 3} d u
\]
for some numbers $a, b$, and $c$, where $a
Solution
Step 1 ：The lower limit of the integral in terms of x is 0. We can substitute this into the equation u=5x-2 to find the corresponding lower limit in terms of u, which will be our a.
Step 2 ：Substitute x = 0 into the equation to get a = -2.
Step 3 ：Final Answer: The exact value of a is \(\boxed{-2}\).
From Solvely APP
Solution
Step 1 ：The lower limit of the integral in terms of x is 0. We can substitute this into the equation u=5x-2 to find the corresponding lower limit in terms of u, which will be our a.
Step 2 ：Substitute x = 0 into the equation to get a = -2.
Step 3 ：Final Answer: The exact value of a is \(\boxed{-2}\).
