1. The problem involves understanding the expression \(\sqrt{x}789\int_a^b f(x)\,dx\). 2. Here, \(\sqrt{x}\) means the square root of \(x\), which is \(x^{1/2}\). 3. The number 789 is a constant multiplier. 4. The integral \(\int_a^b f(x)\,dx\) represents the area under the curve of the function \(f(x)\) from \(x=a\) to \(x=b\). 5. The entire expression can be interpreted as \(789 \times \sqrt{x} \times \int_a^b f(x)\,dx\). 6. Without specific values for \(x\), \(a\), \(b\), or the function \(f(x)\), this is the simplified form. 7. If you want to evaluate it, you need to know \(x\), the limits \(a\) and \(b\), and the function \(f(x)\).