calculate median value of a function

Question

need help on this one please ! I already tried to calculate with F(x) = 0.5 but doesn't work

Answer 1

To find the median, you need to find the value of $x$ that satisfies the equation $F_x(x) = 0.5$.

In order to find $F_x(x)$, we must perform the following calculations.

For the range $-4 \lt x \lt -3$, $\int_{-4}^x 0.01u^2du$

For the range $-3 \lt x \lt -2$, $\int_{-4}^{-3} 0.01x^2dx$

For the range $-2 \lt x \lt -1$, $\int_{-4}^{-3} 0.01x^2dx + \int_{-2}^x(0.2u+0.5)du$

For the range $-1 \lt x \lt 2$, $\int_{-4}^{-3} 0.01x^2dx + \int_{-2}^{-1}(0.2x+0.5)dx$

For the range $2 \lt x \lt 3$, $\int_{-4}^{-3} 0.01x^2dx + \int_{-2}^{-1}(0.2x+0.5)dx +\int_{2}^x0.1udu$

For the range $3 \lt x \lt 7$, $\int_{-4}^{-3} 0.01x^2dx + \int_{-2}^{-1}(0.2x+0.5)dx +\int_{2}^30.1u du + \int_{3}^ucx^4du$

From this you'll have your $F_x(x)$. For each range, find the $x$ which satisfies $F_x(x) = 0.5$, and if $x$ lies in your permitted range, then there you have it!