# Use areas to evaluate the integral.\int_{a}^{11b}2s\ ds, 0<a<b

Use areas to evaluate the integral.

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Step 1
Consider the integrals,

Step 2
To solve the given integrals,
${\int }_{a}^{11b}2sds=2{\int }_{a}^{11b}sds$
$=2{\left[\frac{{s}^{2}}{2}\right]}_{a}^{11b}$
$=2\cdot \frac{1}{2}\cdot {\left[{s}^{2}\right]}_{a}^{11b}$
$={\left(11b\right)}^{2}-{a}^{2}$
$=121{b}^{2}-{a}^{2}$

Jeffrey Jordon