What is the integral from-3 to 1 of x/(sqrt(9-x^2)) ?

The integral from-3 to 1 of x/(sqrt(9-x^2)) is -2sqrt(2)

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integral from-3 to 1 of x/(sqrt(9-x^2))

\int_{- 3}^{1} \frac{x}{9 - x ^{2}} d x

- 22

Decimal Notation

- 2.82842 \dots

Solution steps

\int_{- 3}^{1} \frac{x}{9 - x ^{2}} d x

Apply u-substitution

: \int_{0}^{8} - \frac{1}{2 u} d u

= \int_{0}^{8} - \frac{1}{2 u} d u

Take the constant out:

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

= - \frac{1}{2} \cdot \int_{0}^{8} \frac{1}{u} d u

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{0}^{8}

= - \frac{1}{2} [2 u^{\frac{1}{2}}]_{0}^{8}

Apply radical rule:

= - \frac{1}{2} [2 u]_{0}^{8}

Compute the boundaries:

42

= - \frac{1}{2} \cdot 42

Simplify

= - 22

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What is the integral from-3 to 1 of x/(sqrt(9-x^2)) ?
The integral from-3 to 1 of x/(sqrt(9-x^2)) is -2sqrt(2)