How do I evaluate the following: $$\int_{k_l}^{v_1}g_l(v)vdv-c\int_{k_{l}}^{v_{1}}g_l(v)dv$$ Where $g_l(v)$ is the pdf of random variable $v$, with support $[v_0,v_1].$ Both $k_l$ and $c$ are in $\mathbb{R}^+$. I know that the second term will evaluate to $G_l(v_1)-G_l(k_l)$, but I am not sure about the first. Thank you.
2026-03-18 10:30:03.1773829803
Evaluating the definite integral of the product of a random variable and its PDF over a subset of the support
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