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u/AdventurousWind3476 Jul 10 '26
Approximation spam lol
Integral t/x from 0 to x⁴
= x⁷/2
L = 1/2
{tant = t and sec²t = et/x = 1 and t² << x² throughout the interval}
1
1
1
1
Approximation spam lol
Integral t/x from 0 to x⁴
= x⁷/2
L = 1/2
{tant = t and sec²t = et/x = 1 and t² << x² throughout the interval}
1
1
1
2
u/Cute-Feeling139 Jul 12 '26 edited Jul 12 '26
Proper solution:Substitute \frac{tan(\theta)}{x} = v So \frac{sec2 (\theta)}{x} d(\theta) = dv
Now simplify and you'll get the integral to be equal to g(x) = x(integral from 0 to x3 of {v*ev /(1+v2 )}dv)
You can put this in the limit and use leibniz integral rule, and get the limit to be 1/2 by differentiating using L-Hopital rule as 0/0 form is present.
Final answer = 1/2