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find a lower bound of the integral of x exp(-xt)/(t+1) dt from 0 to 1 when x g...

Feb 4, 2024

find a lower bound of the integral of x exp(-xt)/(t+1) dt from 0 to 1 when x goes to +infinite I want to find a lower bound which tends to 1 when x goes to +infinite

Solution by Steps

step 1

Evaluate the given integral as

x

approaches infinity

step 2

The integral is

\lim_{x \to \infty} \int_0^1 \frac{x e^{-xt}}{t+1} \, dt

step 3

The result of the integral as

x

approaches infinity is given by the asksia-ll calculator as 1

step 4

Therefore, the lower bound of the integral that tends to 1 as

x

goes to infinity is 1

Answer

The lower bound of the integral is 1.

Key Concept

Limit of an integral as a parameter approaches infinity

Explanation

The asksia-ll calculator has determined that the limit of the given integral as

x

approaches infinity is 1, which serves as the lower bound we are seeking.