What is the arc length of $f(x)= e^(3x) +x^2e^x$ on $x in [1,2]$ ?

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Answer 1 · 2017-08-19T13:25:17

The arc length $s$ of the curve $f$ on $x in[a,b]$ is given by

$s=int_a^bsqrt(1+(f'(x))^2)dx$

Here, $f(x)=e^(3x)+x^2e^x$ so $f'(x)=3e^(2x)+2xe^x+x^2e^x$ . The arc length is then:

$s=int_1^2sqrt(1+(3e^(2x)+2xe^x+x^2e^x)^2)dx$

Put this into an online graphing service like WolframAlpha or into any other calculator to find an approximation for the integral:

$sapproxcolor(blue)97.658636$

What is the arc length of f(x)= e^(3x) +x^2e^x f(x)= e^(3x) +x^2e^x on x in [1,2] x in [1,2] ?