How did the last line come from integration?

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Daniyel Yaacov Bilar

IYH Dear Rupa Akter

I ran your question against a Google AI w image recognition. Here is the full explanation https://poe.com/s/xdXDUYU2cjl1myfpxOua

tl/dr λ₁ in the Numerator: The key point is that the final expression involves a product. While each individual integral resulted in λᵢ in the numerator, the product includes the term from i=2. This term has λ₂ in the numerator and (λ₁ + λ₂) in the denominator.

Therefore, the final expression does indeed have λ₁ in the numerator, but it comes from the (i=2) term in the product, not from the integration of a single term.

Rupa Akter

i still didn't get why the product from i=2 to n will make \lambda_1? what is the reason? Daniyel Yaacov Bilar the answer from AI is confusing me.

Marius Ole Johansen

Rupa Akter You are absolutely correct (I have no idea what the AI is yapping about), the final integral has lambda_i in the numerator. It's either a typo or an incorrect "relabeling".