Probability from a piecewise density with unknown power

Let $X$ be a random variable with the probability density function

$$f(x)=\begin{cases}4x^k, & 0<x<1,\ x-\dfrac{x^2}2, & 1\le x<2,\ 0, & \text{otherwise,}\end{cases}$$

where $k$ is a positive integer. Then $P\left(\frac12<X<\frac32\right)$ equals ____________ (round off to 2 decimal places)