Primitive of Power/Examples/x

Example of Use of Primitive of Power

$\ds \int x \rd x = \dfrac {x^2} 2 + C$


Proof

\(\ds \ds \int x \rd x\) \(=\) \(\ds \ds \int x^1 \rd x\)
\(\ds \) \(=\) \(\ds \dfrac {x^{1 + 1} } {1 + 1} + C\) Primitive of Power: $n = 1$
\(\ds \) \(=\) \(\ds \dfrac {x^2} 2 + C\) simplifying

$\blacksquare$


Sources

  • 1937: Eric Temple Bell: Men of Mathematics ... (previous) ... (next): Chapter $\text{VI}$: On the Seashore
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