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

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

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

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

- \frac{π}{2}

Decimal

- 1.57079 \dots

Solution steps

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

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

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

= 0 - \frac{π}{2}

Simplify

= - \frac{π}{2}

y = (x^{6} - 10) x

\int sin^{5} (x) cos^{8} (x) d x

n = 3 \sum \infty \frac{1}{n ^{2} - 1}

\frac{s}{( s ^{2} + 9 ) ^{2}}

y = \frac{1}{4 - x}

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