What is the integral from-3 to 0 of x/(sqrt(9-x^2)) ?

The integral from-3 to 0 of x/(sqrt(9-x^2)) is -3

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integral from-3 to 0 of x/(sqrt(9-x^2))

\int_{- 3}^{0} \frac{x}{9 - x ^{2}} d x

- 3

Solution steps

\int_{- 3}^{0} \frac{x}{9 - x ^{2}} d x

Apply u-substitution

: \int_{0}^{9} - \frac{1}{2 u} d u

= \int_{0}^{9} - \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}^{9} \frac{1}{u} d u

Apply the Power Rule

: [2 u^{\frac{1}{2}}]_{0}^{9}

= - \frac{1}{2} [2 u^{\frac{1}{2}}]_{0}^{9}

Apply radical rule:

= - \frac{1}{2} [2 u]_{0}^{9}

Compute the boundaries:

6

= - \frac{1}{2} \cdot 6

Simplify

= - 3

y = x, y = \frac{1}{3} x, x = 25

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What is the integral from-3 to 0 of x/(sqrt(9-x^2)) ?
The integral from-3 to 0 of x/(sqrt(9-x^2)) is -3