People respond well to perceived effort and investment on the part of others. When I get an email that is worded poorly from a colleague, or start reading a paper that has not been carefully revised, I am more likely to tune out and abandon the situation.
It is possible that you put significant effort into creating this question, but when I read it, it feels like a question that was thrown out to me in first draft form. If a professor gave me this question, I would feel that it is unlikely that the question is even possible, let alone good. Additionally, your opinion of the students is clearly low as shown by your comments, and the students are going to be able to detect that.
I would say the question is basically impossible as written, not because of the math, but because of the social cues above.
Here is what happens when I try to read this question:
The two sides of an isosceles triangle have a length of l, each side,
What is meant by "the two sides of a triangle?" Triangles have three sides. "The" here indicates that these two sides are the only two sides. That's not true. From context I guess you don't care which two sides, but the word "the" starts off the sentence with confusion. Then, what is "each side" doing in this question? It doesn't clarify anything. Maybe you were worried I would think that two of the sides had a total length of $l$? Then you would have used the word "total."
I am fourteen words into the question and I have already had to stop three times to figure out what is being asked. As a student, I am somewhat hostile already: the person writing the question did not take much effort to communicate with me. All of this effort could have been avoided if the instructor had drawn a picture of a triangle, or revised the first draft of the question. I do not have high hopes.
the angle between them is the value of a random variable called "x" with a function of proportional density to x(π - x) in each point x ∈ (0, π/2).
What? At this point, in a timed test, I am looking for a different question. This question is either here to try to get me to waste time, or it is here for some other student to get correct -- it's certainly not for me.
Calculate the function of density of the area of the triangle
I do not know what this is and I don't know any student that would know what this is.
If you want to ask students this question, you need to work hard on revising it to communicate what you are asking. Here is a second draft of the first couple of sentences, which at least communicate the triangle you have in mind without requiring significant mental effort on the part of students who already know you don't expect them to get the question correct:
Two sides of an isosceles triangle each have length $l$. The angle between these two sides is given by $x$, which is between $0$ and $\pi/2$.