# How to find the value of $k$ for the density function defined by $f(x)=kx^2$?

Suppose $x$ is a continuous random variable. The probability density function of $x$ is $f(x) = kx^2$ when $0 < x < 2$ and $f(x)= 0$ otherwise. What is the value of $k$?

More info: Does this mean I find value under the curve of $P(0 <x <2)$?

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## migrated from mathematica.stackexchange.comJun 5 '13 at 19:13

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Hint: If $f(x)$ is a pdf then it must be the case that $\int_0^2{f(x)dx}=1$. Use this fact to find out the value of $k$.