What is the arc length of $f (x) = {(x^{3} + x)}^{5}$ $f(x)=(x^3 + x)^5$ in the interval $[2, 3]$ $[2,3]$ ?

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Answer 1 · 2018-06-25T12:12:35

$\approx 2.42 \cdot 10^{7}$ $approx 2.42*10^7$

We Need the Formula

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

we have
$f'(x)=5(x^3+x)^4(3x^2+1)$
so our integral is given by

$int_2^3sqrt(1+(5(x^3+x)^4(3x^2+1))^2)dx$
this is $approx 2.42*10^7$

What is the arc length of f(x)=(x^3 + x)^5 f(x)=(x3+x)5f(x)=(x^3 + x)^5 in the interval [2,3][2,3][2,3]?