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

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Answer 1 · 2017-04-15T17:51:54

#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#