Find the length of the curve

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MarkSA

Junior Member
Joined
Sep 8, 2007
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243
Hello,

Find the length of the curve of:
y = (x^5)/6 + 1/(10x^3)
with 1 <= x <= 2

I'm to this point:
L = integral from 1 to 2 of: sqrt(1 + [(5/6)* x^4 - (1/10)* 1/(x^4)]^2)dx

I can square the inside mess to 1 + (25/36)*x^8 + (9/100)*(1/x^8) + 1/2, but that doesn't seem to get me anywhere. I'm not too sure how to solve it from here. Any ideas?

Also, regarding another problem.. I have a similar mess of an integral from 1 to 3 of: sqrt(1 + (x^4)/4)dx. Would the only way to evaluate that one be simpson's rule approximation?

Thanks
 
MarkSA said:
Hello,

Find the length of the curve of:
y = (x^5)/6 + 1/(10x^3)
with 1 <= x <= 2

I'm to this point:
L = integral from 1 to 2 of: sqrt(1 + [(5/6)* x^4 - (3/10)* 1/(x^4)]^2)dx

I can square the inside mess to 1 + (25/36)*x^8 + (9/100)*(1/x^8) - 1/2, <<<< This is a perfect square>>>[(5/6)* x^4 + (1/10)* 1/(x^4)]^2


but that doesn't seem to get me anywhere. I'm not too sure how to solve it from here. Any ideas?

Also, regarding another problem.. I have a similar mess of an integral from 1 to 3 of: sqrt(1 + (x^4)/4)dx.

Would the only way to evaluate that one be simpson's rule approximation? <<< No - judicious trig substitution (or use of CAS calculator) will do it

Thanks
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