What is the integral from 0 to 3 of xsqrt(10-x^2) ?

The integral from 0 to 3 of xsqrt(10-x^2) is (10sqrt(10)-1)/3

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integral from 0 to 3 of xsqrt(10-x^2)

\int_{0}^{3} x 10 - x^{2} d x

\frac{10 10 - 1}{3}

Decimal Notation

10.20759 \dots

Solution steps

\int_{0}^{3} x 10 - x^{2} d x

Apply u-substitution

: \int_{10}^{1} - \frac{u}{2} d u

= \int_{10}^{1} - \frac{u}{2} d u

\int_{a}^{b} f (x) d x = - \int_{b}^{a} f (x) d x, a < b

= - \int_{1}^{10} - \frac{u}{2} 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_{1}^{10} u d u)

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{10}

= - (- \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{10})

Simplify

= \frac{1}{2} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{10}

Compute the boundaries:

\frac{20 10}{3} - \frac{2}{3}

= \frac{1}{2} (\frac{20 10}{3} - \frac{2}{3})

Simplify

= \frac{10 10 - 1}{3}

\frac{8 x}{7 - tan ( x )}

x \to \infty lim (\frac{- 1}{2})

f (x) = x + 1 (1 - 5 x^{2})^{8}

\int \frac{1}{49 - x ^{2}} d x

y^{^{'}} = - y sin (2 x)

What is the integral from 0 to 3 of xsqrt(10-x^2) ?
The integral from 0 to 3 of xsqrt(10-x^2) is (10sqrt(10)-1)/3