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The problem is asking for an approximation of the integral \(\int_0^{12} f(x) dx\) using the midpoint rule with six rectangles, denoted by \(M_6\).

### Midpoint Rule:
The midpoint rule for approximating an integral \(\int_a^b f(x) dx\) is given by:
\[
M_n = \sum_{i=1}^{n} f(\text{midpoint}_i) \cdot \Delta x
\]
where:


Draw six rectangles with sample points as midpoints (M6). Then use the six rectangles to approximate the value of the integral ∫₀¹² f(x) dx.

Learn how to approximate the integral ∫₀¹² f(x) dx using the midpoint rule with six rectangles (M6). This step-by-step solution explains the process of calculating the integral approximation, using key concepts such as the midpoint rule and interval subdivision. Suitable for advanced high school or early college students.

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