# Cool integral

**Calculus**Level 4

\[ \int_1^3 \dfrac{dx}{\sqrt{(x-1)(3-x)}} = \, ? \]

Round your answer to the nearest hundredth.

**Bonus**: Generalize \( \displaystyle \int_a^b \dfrac{dx}{\sqrt{(x-a)(b-x)}} \).

\[ \int_1^3 \dfrac{dx}{\sqrt{(x-1)(3-x)}} = \, ? \]

Round your answer to the nearest hundredth.

**Bonus**: Generalize \( \displaystyle \int_a^b \dfrac{dx}{\sqrt{(x-a)(b-x)}} \).

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