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Question Number 198052 by Mastermind last updated on 09/Oct/23

Answered by Sutrisno last updated on 09/Oct/23

$$x=asin\theta \Rightarrow dx=acos\theta d\theta$$$${\int }_0^{\frac{\pi }{6}}{a}^2{sin}^2\theta {(a^2-a^2{sin}^2\theta )}^{-\frac{3}{2}}acos\theta d\theta$$$${\int }_0^{\frac{\pi }{6}}{a}^2{sin}^{2}x{\left(a^2{cos}^2\theta \right)}^{-\frac{3}{2}}acos\theta d\theta$$$${\int }_0^{\frac{\pi }{6}}{a}^2{sin}^2{xa}^{-3}{cos}^{-3}\theta acos\theta d\theta$$$${\int }_0^{\frac{\pi }{6}}{tan}^2\theta d\theta$$$${\int }_0^{\frac{\pi }{6}}{sec}^2\theta -1d\theta$$$$tan\theta -\theta {\mid }_0^{\frac{\pi }{6}}$$$$\frac{\sqrt{3}}{3}-\frac{\pi }{6}$$$$$$

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