Let the function f: [0, 2] → ℝ be defined as: f(x) = e^min{x², x - ⌊ x ⌋}, x ∈ [0, 1), e^(⌊ x - logₑ x ⌋), x ∈…

Question

Let the function $$f : [0, 2] 	o \mathbb{R}$$ be defined as:
$$ f(x) = \begin{cases} e^{\min\{x^2, x - \lfloor x floor\}}, & x \in [0, 1),\ e^{\lfloor x - \log_e x floor}, & x \in [1, 2), \end{cases} $$
where $$\lfloor t floor$$ denotes the greatest integer less than or equal to $$t$$.

Then the value of the integral $$\int_0^2 x f(x) \, dx$$ is:

Accepted Answer

C. $$2e - \frac{1}{2}$$

Answer

A. $$\left(e - 1\right) \left(e^2 + \frac{1}{2}\right)$$

Answer

B. $$1 + \frac{3e}{2}$$

Answer

D. $$2e - 1$$

Answer & step-by-step solution

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