# Piecewise Functions - 6

Calculus Level 5

Consider a function $$f : \mathbb{R} \rightarrow \mathbb{R}$$ defined as:

$f(x) = \begin{cases}\displaystyle\int\limits_ {|x|} ^{x^2} \ln t~ dt & \text{if } x \leq a \\ \displaystyle\int\limits_ {a} ^{x} e^t \sin t~ dt & \text{if } x > a\end{cases}$

Let $$a_1, a_2, a_3 ...... a_n$$ be the values of $$a$$ for which $$f$$ is continuous throughout its domain.

Find

$\displaystyle\prod_{i = 1} ^ n (a_i- 2)^2$

Note: If you think there are no values of $$a$$ satisfying the conditions, enter your answer as 999.

This problem is part of the set - Piecewise-defined Functions

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