What is the arclength of $f (x) = x sin 3 x$ $f(x)=xsin3x$ on $x \in [3, 4]$ $x in [3,4]$ ?

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Answer 1 · 2018-07-09T13:26:31

$\approx 6.578961133$ $approx 6.578961133$

Given is
$f (x) = x sin (3 x)$ $f(x)=xsin(3x)$
We Need the product and the chain rule:

$f'(x)=sin(3x)+3xcos(3x)$ so we have evaluate the following integral

$int_3^4sqrt(1+(sin(3x)+3xcos(3x))^2)dx$
a numerical method gives us

$approx 6.578961133$

What is the arclength of f(x)=xsin3xf(x)=xsin3xf(x)=xsin3x on x in [3,4]x∈[3,4]x in [3,4]?