# What is the midpoint of a segment whose endpoints are (3, -1) and (-5, -3)?

Uriel Hartman 2022-11-19 Answered
What is the midpoint of a segment whose endpoints are (3, -1) and (-5, -3)?
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Answer: $\int \frac{\frac{\mathbf{4}}{\mathbf{7}}\mathbf{+}{\mathbf{x}}^{\mathbf{3}\mathbf{/}\mathbf{4}}}{\sqrt{\mathbf{4}\mathbf{-}\mathbf{x}\mathbf{-}{\mathbf{x}}^{\mathbf{7}\mathbf{/}\mathbf{4}}}}\phantom{\rule{thinmathspace}{0ex}}dx$
Let $\mathbf{u}\mathbf{=}\mathbf{4}\mathbf{-}\mathbf{x}\mathbf{-}{\mathbf{x}}^{\mathbf{7}\mathbf{/}\mathbf{4}}\phantom{\rule{thinmathspace}{0ex}}$
You should end up with
$\mathbf{-}\frac{\mathbf{4}}{\mathbf{7}}\int \frac{\mathbf{d}\mathbf{u}}{\sqrt{\mathbf{u}}}$
after substituting.
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