Given the definite integral:
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the solutions to the problems:
10. (b) Find the value of $m$
Given the definite integral:
$$ \int_{-2}^{m} (4x^2 - 2x + 9)\,dx = \frac{172}{3} $$
where $m$ is an integer.
Step 1: Integrate the function $4x^2 - 2x + 9$.
$$ \int (4x^2 - 2x + 9)\,dx = \frac{4x^3}{3} - \frac{2x^2}{2} + 9x = \frac{4x^3}{3} - x^2 + 9x $$
Step 2: Evaluate
