1)a) Find a value C so that p(x) = C√(24 + x) is a probability density function on the interval

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1)a) Find a value C so that $p(x) = C\sqrt{24 + x}$ is a probability density function on the interval $[1, 12]$. b) Compute the probability $P(5 \le X \le 10)$. 2) Calculate the length of the curve $y = \frac{1}{3}x^{3/2}$ on the interval $16 \le x \le 25$.