What is the integral from-1 to 0 of (2+sqrt(1-x^2)) ?

The integral from-1 to 0 of (2+sqrt(1-x^2)) is 2+pi/4

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integral from-1 to 0 of (2+sqrt(1-x^2))

\int_{- 1}^{0} (2 + 1 - x^{2}) d x

2 + \frac{π}{4}

Decimal Notation

2.78539 \dots

Solution steps

\int_{- 1}^{0} 2 + 1 - x^{2} 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}^{0} 2 d x + \int_{- 1}^{0} 1 - x^{2} d x

\int_{- 1}^{0} 2 d x = 2

\int_{- 1}^{0} 1 - x^{2} d x = \frac{π}{4}

= 2 + \frac{π}{4}

\int_{0}^{4} (2 + x) d x

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

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

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

\int_{1}^{4} 5^{2 x} d x

What is the integral from-1 to 0 of (2+sqrt(1-x^2)) ?
The integral from-1 to 0 of (2+sqrt(1-x^2)) is 2+pi/4