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

The integral from-1 to 0 of xsqrt(1-x^2) is -1/3

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

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

- \frac{1}{3}

Decimal Notation

- 0.33333 \dots

Solution steps

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

Apply u-substitution

: \int_{0}^{1} - u^{2} d u

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Apply the Power Rule

: [\frac{u ^{3}}{3}]_{0}^{1}

= - [\frac{u ^{3}}{3}]_{0}^{1}

Compute the boundaries:

\frac{1}{3}

= - \frac{1}{3}

\frac{d}{d x} (a (sin (x) - x cos (x)))

\int x ln (x - 2) d x

\int \frac{e ^{x}}{1 - e ^{x}} d x

\frac{d}{d x} (x 3 - 2 x^{2})

\int_{0}^{1} 4 (1 + x)^{7} d x

What is the integral from-1 to 0 of xsqrt(1-x^2) ?
The integral from-1 to 0 of xsqrt(1-x^2) is -1/3