What is the limit of the expression \(\lim_{n\to\infty}\sum_{i=1}^n\left(\sqrt{77+\frac{i}{n}}\cdot\frac{10}{n}\right)\)?

A) \(\int_0^1 \sqrt{77+x}dx \cdot \int_0^1 \sqrt{77+x}dx \cdot \int_0^1 \sqrt{77-x}dx \cdot \int_0^1 \sqrt{77-x}dx\)
B) \(\int_0^1 \sqrt{77+x}dx \cdot \int_0^1 \sqrt{77+x}dx \cdot \int_0^1 \sqrt{78+x}dx \cdot \int_0^1 \sqrt{77-x}dx\)
C) \(\int_0^1 \sqrt{77+x}dx \cdot \int_0^1 \sqrt{77+x}dx \cdot \int_0^1 \sqrt{77-x}dx\)
D) \(\int_0^1 \sqrt{77-x}dx \cdot \int_0^1 \sqrt{77-x}dx \cdot \int_0^1 \sqrt{78+x}dx \cdot \int_0^1 \sqrt{77-x}dx\)