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# Area under the curve

### Example 1

Find the area between $$y=7-x^2$$ and the $$x$$-axis between the values $$x=-1$$ and $$x=2$$.

Firstly, draw the graph:

The area will be:

\begin{eqnarray*}
&&\int_{-1}^2 7-x^2 \; \mathrm{d} x \\
&=& \left[ 7x - \frac{x^3}{3} \right]_{-1}^2 \\
&=& \left[ 7\times 2 - \frac{2^3}{3} \right] - \left[7\times -1 - \frac{(-1)^3}{3} \right] \\
&=& 18
\end{eqnarray*}