(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

[tex]

18\int_0^4 \sqrt{4- (y-2)^2}dy

[/tex]

2. Relevant equations

According to the textbook l am supposed to use [tex]y=2sin\theta [/tex] for substitution

3. The attempt at a solution

[tex]y=2sin\theta [/tex]

[tex]dy=2cos\theta d\theta [/tex]

[tex]

18\int_0^4 \sqrt{4- (2sin\theta-2)^2}2cos\theta d\theta

[/tex]

( I am stuck at converting the limits of my integral using [tex]y=2sin\theta [/tex] )

[tex]

18\int_0^4 \sqrt{4- (4sin^2\theta-4sin\theta-4sin\theta+4)}2cos\theta d\theta

[/tex]

[tex]

18\int_0^4 \sqrt{4- (4sin^2\theta-8sin\theta+4)}2cos\theta d\theta

[/tex]

( How do l simplify this integral )

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# How do l integrate this ?

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