<s>[INST] Take an example of Integrate of root I want to solve an example like this : $\int_{0}^{4}\sqrt{4^2-x^2}\ dx$ according to this equation :$$\int \sqrt{a^2-x^2}\ dx= \frac{1}{2}\left(x\sqrt{a^2-x^2}+a^2\sin^{-1}\left(\frac{x}{a}\right)\right)$$ 
I have problem with that sine . I want to see the solving step by step.
 [/INST] Notice, applying the standard formula we get 
$$\int_{0}^{4}\sqrt{4^2-x^2}dx=\frac{1}{2}\left(x\sqrt{4^2-x^2}+4^2\sin^{-1}\left(\frac{x}{4}\right)\right)_{0}^{4}$$ $\color{red}{\text{applying the limits}}$ $$=\frac{1}{2}\left(4\sqrt{4^2-4^2}+4^2\sin^{-1}\left(\frac{4}{4}\right)-(0)\sqrt{4^2-(0)^2}-4^2\sin^{-1}\left(\frac{0}{4}\right)\right)$$ $$=\frac{1}{2}\left(16\sin^{-1}(1)\right)$$ $$=\frac{1}{2}\left(16\frac{\pi}{2}\right)=4\pi$$
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