What is the arc length of teh curve given by $f (x) = 3 x^{6} + 4 x$ $f(x)=3x^6 + 4x$ in the interval $x \in [- 2, 184]$ $x in [-2,184]$ ?

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Answer 1 · 2017-04-15T17:51:54

$L = 1.16 \times 10^{14}$ $L=1.16xx10^14$

To find arc length, we use the equation:

$L=int_a^b sqrt(1+f'(x)^2)dx$

Take the derivative of $f(x)$ :

$f'(x)=18x^5+4$

Now plug into the formula with the interval:

$int_-2^184 sqrt(1+(18x^5+4)^2)dx$

Solve inside the parentheses:

$int_-2^184 sqrt(1+324x^10+144x^5+16)dx$

Simplify inside the square root:

$int_-2^184 sqrt(324x^10+144x^5+17)dx$

Solve the integral:

$L=1.16xx10^14$

What is the arc length of teh curve given by f(x)=3x^6 + 4xf(x)=3x6+4xf(x)=3x^6 + 4x in the interval x in [-2,184]x∈[−2,184]x in [-2,184]?