What is the definite integral of $e^(2x)$ from -2 to 2?

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Answer 1 · 2014-09-25T04:23:56

$int_(-2)^(2)e^(2x)dx$

Let $u=2x$

$du=2 dx$

$(du)/2=(2 dx)/2$

$(du)/2=dx$

$inte^(u)*(du)/2=1/2inte^udu$

Calculate the new boundaries

Upper Bound = $2$

$u=2x=2(2)=4$

Lower Bound = $-2$

$u=2x=2(-2)=-4$

$1/2int_(-4)^(4)e^udu$

$=1/2[e^u]_(-4)^(4)$

$=1/2[e^(4)-e^(-4)]$

$=1/2[e^(4)-1/e^(4)]$

$=[e^(4)/2-1/(2e^(4))]$

$=27.2899172$

What is the definite integral of e^(2x)e^(2x) from -2 to 2?