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Question 14

\begin{align} \int\left(1-x\right).\sqrt {x}.dx\end{align}

Answer

\begin{align} \int\left(1-x\right).\sqrt {x}.dx\end{align}

\begin{align} =\int \left(\sqrt {x} - x^\frac32\right).dx\end{align}

\begin{align} =\frac{x^{\displaystyle\frac32}}{\displaystyle\frac32} - \frac{x^{\displaystyle\frac52}}{\displaystyle\frac52}+C \end{align}

\begin{align} =\frac23\;x^\frac32\; - \frac25\;x^\frac52\;+C \end{align}

 

 

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