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

The integral of-xsqrt(1-x^2) is 1/3 (1-x^2)^{3/2}+C

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integral of-xsqrt(1-x^2)

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

\frac{1}{3} (1 - x^{2})^{\frac{3}{2}} + C

Solution steps

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

Take the constant out:

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

= - \int x 1 - x^{2} d x

Apply u-substitution

: \int - u^{2} d u

= - \int - u^{2} d u

Take the constant out:

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

= - (- \int u^{2} d u)

Apply the Power Rule

: \frac{u ^{3}}{3}

= - (- \frac{u ^{3}}{3})

Substitute back

u = 1 - x^{2}

= - (- \frac{( 1 - x ^{2} ) ^{3}}{3})

Simplify

- (- \frac{( 1 - x ^{2} ) ^{3}}{3}) : \frac{1}{3} (1 - x^{2})^{\frac{3}{2}}

= \frac{1}{3} (1 - x^{2})^{\frac{3}{2}}

Add a constant to the solution

= \frac{1}{3} (1 - x^{2})^{\frac{3}{2}} + C

\frac{d}{d x} (- x + 4)

x \to - 1 + lim (x^{2})

\frac{d}{d t} (π r (t) (t)^{2} h)

\int (x + 1)^{2} e^{x} d x

\int \frac{1}{2 x + 4} d x

What is the integral of-xsqrt(1-x^2) ?
The integral of-xsqrt(1-x^2) is 1/3 (1-x^2)^{3/2}+C