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$\int _{ 10 }^{ 13 }{ 2x } dx\quad =\quad { { x }^{ 2 }\quad }_{ 10 }^{ 13 }\quad =\quad { 13 }^{ 2 }\quad -\quad { 10 }^{ 2 }\quad =\quad 169\quad -\quad 100\quad =\quad \boxed { 69 }$

Before even attempting to solve it I typed in 69 and voila!

$\displaystyle \int_{10}^{13} {2x}\text{ dx}=x^2 |_{10}^{13}=169-100=\boxed{69}$

=x^2 =13^2-10^2 =(13+10)(13-10) =(23)(3) =69

The antiderivative of $2x$ is $x^2+C$ my excellent stallion. Then the difference of squares is $23*3$ . 69 dudes!

integrate 2x get (2x^2)/2 so its X^2 (definite integral omit constant) Then 13^2 - 10^2 = 69

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