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

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

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

\int_{- 1}^{1} (1 - x^{2} + 1) d x

\frac{π}{2} + 2

Decimal

3.57079 \dots

Solution steps

\int_{- 1}^{1} 1 - x^{2} + 1 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}^{1} 1 - x^{2} d x + \int_{- 1}^{1} 1 d x

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

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

= \frac{π}{2} + 2

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