Question

Let the function f: [0,2] $\rightarrow$ R be defined as $f(x) = \begin{cases} e^{min}{x^2,x-[x]} & \quad x \in[0,1]\\\ e^{[x-log_ex]} & \quad x\in[1,2] \end{cases}$
where [t] denotes the greatest integer less than or equal to t. Then the value of the integral $\int^2_0xf(x)dx$ is

• A. $\bigg(e^2+\frac{1}{2}\bigg)$
• B. 2e-1
• C. $1+\frac{3e}{2}$
• D. $2e-\frac{1}{2}$

Answer 1

Answer: (D)

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

Answer 2

The Correct Option is(D):$2e-\frac{1}{2}$