the problem is this(adsbygoogle = window.adsbygoogle || []).push({});

[tex]f(x)=\int_{1/2}^{sin^2x} \frac{ cos^2t }{ t^2-t }dt - \int_{1/2}^{cos^2x} \frac{sin^2(1-t]}{t^2-t}dt [/tex]

solve [tex] f(\frac{\pi}{3}) [/tex]

They begin by doing the substitution s=1-t on the second integral and it leads to [tex]t^2-t=s^2-s[/tex] and [tex] dt=-ds[/tex]

this leads to the 2 integrals

[tex]f(\frac{\pi}{3})=\int_{1/2}^{3/2} \frac{cos^2t}{t^2-t}dt + \int_{1/2}^{3/2} \frac{sin^2s}{s^2-s}ds [/tex]

they then just make it into

[tex]f(\frac{\pi}{3})=\int_{1/2}^{3/2} \frac{1}{t^2-t}dt[/tex]

Solving that one is a pieace of cake

but its this last step I dont follow. Why can I say that [tex] sin^2s+cos^2t=1[/tex]? How can it be 1 when its 2 different variables??

and why is [tex] t^2-t=s^2-s [/tex] Why can I just replace the s with t's when s isnt equal to t???

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# Homework Help: Help me understand this solution

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