How to form an equation for probability based on the following graph?

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enter image description here

The y-axis is the probability density function of x( a continuous random variable).

Here's the solution I tried: formula

Is this correct?

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Yes.

You could also just calculate the area of the triangle (that is what the integral does) and say it is equal to 1.

$$ \dfrac{(8*k)}{2 }= 4k = 1 => k = \dfrac{1}{4} $$

For problems with more complicated functions, to use the integral is your only option.