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TOKYO-349 lets solve it step by step **Understanding the Problem** We need to evaluate the expression `∫[0 to 1] (x`** using the Midpoint Rule. The integral is to be approximated over `(a)`, which means `(b)`. **Key Information** - The integral is from `0` to `1`. - The Midpoint Rule is used to approximate the integral. - We need to find out how many rectangles (number of partitions) are used in the rule. **Breaking Down the Problem** 1. **Evaluate integral using Midpoint Rule** - The integral is `∫[0 to 1] (x`**`. We'll need to find the area under the curve `y = x`** from `0` to `1`. - The Midpoint Rule will approximate this area by calculating the areas of the rectangles under the curve. 2. **Number of partitions** - The problem mentions `(a)`, which signifies `(b)`. This implies that we are to calculate the integral using `(a)` partitions. - We need to figure out what `(a)` is. Since it's included in `(b)`, we'll assume it represents the number of partitions. **Calculations** 1. **Calculate area using Midpoint Rule** - First, we'll divide the interval from `0` to `1` into `(a)` partitions. Each partition will have a width of `1 / (a)`. - For each partition, the midpoint will be `(0 + 1 / (a)) / 2`, `(1 / (a) + 2 / (a)) / 2`, ... up to `((a - 1) / (a) + 1) / 2`. - These midpoints will be used to determine the height of each rectangle, which is `x`**`. - The total area will be the sum of the areas of these rectangles. 2. **Calculate number of partitions** - The number of partitions `(a)` is specified as `(b)`. Since `(b)` is `(a)`, we'll conclude that `(a) is equal to **(b)`. - So, the number of partitions is `**(b)`. **Conclusion** The integral is approximated using `**(b)` rectangles under the Midpoint Rule. **Final Answer** `**(b)`

2015年11月8日88 分