What is the arc length of $f (x) = 10 + \frac{x^{\frac{3}{2}}}{2}$ $f(x)=10+x^(3/2)/2$ on $x \in [0, 2]$ $x in [0,2]$ ?

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Answer 1 · 2018-03-15T08:30:51

$L = \frac{1}{27} (17 \sqrt{34} - 32)$ $L=1/27(17sqrt34-32)$ units.

$f (x) = 10 + \frac{1}{2} x^{\frac{3}{2}}$ $f(x)=10+1/2x^(3/2)$

$f'(x)=3/4sqrtx$

Arc length is given by:

$L=int_0^2sqrt(1+9/16x)dx$

Integrate directly:

$L=32/27[(1+9/16x)^(3/2)]_0^2$

Insert the limits of integration:

$L=32/27((17/8)^(3/2)-1)$

Simplify:

$L=1/27(17sqrt34-32)$

What is the arc length of f(x)=10+x^(3/2)/2f(x)=10+x322f(x)=10+x^(3/2)/2 on x in [0,2]x∈[0,2]x in [0,2]?