Final answer:
To determine the value of the constant c for the probability density function, one would typically integrate the function over the range of x and solve for c so that the total probability equals 1. However, calculus is required to perform this action, and it appears some information or methodology may be missing to solve without it.
Step-by-step explanation:
To find the constant c for the probability density function (pdf) f(x) = c(x^2 + 2x) over the interval 0 ≤ x ≤ 10, we must ensure that the total area under the curve of the function over this interval is 1, representing a total probability of 1.
This involves integrating the function across the interval and solving for c, but the problem specifies to ignore calculus methods.
Hence, without using integration, we consider that the area representing the probability must equal 1 and look for a way to express this through a function or simple algebraic manipulation that doesn't require calculus.
The function provided is a quadratic function multiplied by the constant c.
Without the use of calculus, it's not straightforward to solve for c algebraically.
However, the question appears to be missing some information or a method to determine c without calculus.
Normally, we would integrate f(x) from 0 to 10 to find the area under the curve and then solve for the constant c so that the total area is 1.