A definite integral which shows us how close our approximation is to a transcendental number.

Calculus Level 4

01x4(1x)41+x2dx=A\large \int_0^1 \frac {x^4(1-x)^4}{1+x^2} dx=A

The equation above holds true for real number AA. What is 10000A\lceil 10000A\rceil?

Notation: \lceil \cdot \rceil denotes the ceiling function.

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