What is the integral from 1 to 3 of 1-sqrt(4x-x^2-3) ?

The integral from 1 to 3 of 1-sqrt(4x-x^2-3) is 2-pi/2

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integral from 1 to 3 of 1-sqrt(4x-x^2-3)

\int_{1}^{3} 1 - 4 x - x^{2} - 3 d x

2 - \frac{π}{2}

Solution steps

\int_{1}^{3} 1 - 4 x - x^{2} - 3 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{3} 1 d x - \int_{1}^{3} 4 x - x^{2} - 3 d x

\int_{1}^{3} 1 d x = 2

\int_{1}^{3} 4 x - x^{2} - 3 d x = \frac{π}{2}

= 2 - \frac{π}{2}

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What is the integral from 1 to 3 of 1-sqrt(4x-x^2-3) ?
The integral from 1 to 3 of 1-sqrt(4x-x^2-3) is 2-pi/2