Find the area bounded by (i) y`=log""_(e)|x|andy=0` (ii) `y=|log""_(e)|x||andy=0`
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AI Generated Solution
To solve the given problem, we need to find the area bounded by the curves for both parts of the question.
### Part (i): Find the area bounded by \( y = \log_e |x| \) and \( y = 0 \)
1. **Identify the curves**: The curve \( y = \log_e |x| \) is defined for \( x \neq 0 \). It has two branches: one for \( x > 0 \) and one for \( x < 0 \). The curve approaches negative infinity as \( x \) approaches 0 from either side.
2. **Find the points of intersection**: We need to find where \( y = \log_e |x| \) intersects with \( y = 0 \).
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