Am i being really dumb when struggling to do this?(adsbygoogle = window.adsbygoogle || []).push({});

[tex] L = 4\sqrt{2}c \left \int_{0}^{\frac{\pi}{2}} \left \frac{dt}{\sqrt{1 + sin^2 t}} [/tex]

Using substitution or otherwise show that

[tex] L = 4c \left \int_{0}^{1} \left \frac{du}{\sqrt{1 - u^4}} [/tex]

Its a small part of a question but its stopping me doing the rest. Anyone help me out? The limits im fine with, for the rest i get:

[tex] u = \sin t \left \frac{du}{dt} = \cos t \left dt = \frac{du}{\cos t} \left so \left L = \frac{du}{\sqrt{1 - u^2}\cos t} \left ??? [/tex]

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# Homework Help: Integration substitution

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