1. The expression is \(\sqrt[n]{x}\int_a^b f(x)\,dx\). 2. Here, \(\sqrt[n]{x}\) represents the \(n\)-th root of \(x\), or \(x^{1/n}\). 3. The integral \(\int_a^b f(x)\,dx\) calculates the area under the curve \(f(x)\) from \(a\) to \(b\). 4. The given expression is the product of these two quantities. 5. Without specific functions or values for \(f(x)\), \(a\), \(b\), \(x\), or \(n\), no further simplification is possible. Final answer: \(\sqrt[n]{x}\int_a^b f(x)\,dx = x^{1/n} \times \int_a^b f(x)\,dx\).