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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
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