integration

[cursive pasture]

hi this is for the kids I tutor but for some reason I genuinely
cannot work it oit

[cosmic prairie]

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[warm orchid]

$$dx = C\cos t dt$$

$$\int \sqrt{C^2-x^2}dx = C^2\int |\cos t|\cos t dt $$

[north cypress]

aL

aL

[warm orchid]

$$16\leq x^2 \leq 24 \Rightarrow 16\leq C^2\sin ^2t \leq 24$$

[north cypress]

aL

[warm orchid]

plug in C^2 = 32

$$\frac{1}{2}\leq \sin ^2t \leq \frac{3}{4}$$

[north cypress]

aL

[warm orchid]

that gives you bounds for t

@cursive pastureis that enough to get you started?

conclude that t in (pi/4, pi/3)

and use

$$2\cos ^2t = 1+\cos 2t$$

[north cypress]

aL

[warm orchid]

to integrate

[cursive pasture]

oh yeah

thanks

[warm orchid]

[bold snow]

@cursive pasture

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[cursive pasture]

+close

[bold snow]

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