Write a value

Question:

Write a value of $\int \sqrt{4-\mathrm{x}^{2}} \mathrm{dx}$.

Solution:

we know that $\int \sqrt{a^{2}-x^{2}} d x=\frac{x \sqrt{a^{2}-x^{2}}}{2}+\frac{x^{2}}{2} \sin ^{-1}\left(\frac{x}{a}\right)+c$

Given $\int \sqrt{4-x^{2}}$

$=\int \sqrt{2^{2}-x^{2}}$

$=\frac{x \sqrt{2^{2}-x^{2}}}{2}+\frac{x^{2}}{2} \sin ^{-1}\left(\frac{x}{2}\right)$

$=\frac{x \sqrt{4-x^{2}}}{2}+\frac{x^{2}}{2} \sin ^{-1}\left(\frac{x}{2}\right)+c$

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