The following limit represents the definite integral $\int_a^b f(x)dx$ for some real numbers $a$ and $b$, and an integrable function $f$:
$\lim_{n\to\infty} \sum_{i=1}^n \frac{3i}{n^2}(4+\frac{2i}{n})$
a) Find $\Delta x$ and $x_i$ from this expression and deduce the values of $a$ and $b$, and the function $f$.
FORMATTING: Your expression for $\Delta x$ should be an expression involving $n$. Your expression for $x_i$ should be an expression involving the index $i$ and $n$.
The numbers $a$ and $b$ are real numbers, and $f(x)$ should be a function of $x$. Write your answer in the form $[\Delta x, x_i, a, b, f(x)]$ including the square brackets [] and commas (,) between each term. Strict scientific calculator notation is required in your answer, meaning in particular $\cdot$ for multiplication, e.g. $2x$ must be written $2*x$, and $(x+1)(x+2)$ must be written $(x+1)*(x+2)$.
Answer: $[\Delta x, x_i, a, b, f(x)]=$
