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

The integral from 1 to 3 of xsqrt(3x^2-2) is 124/9

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integral from 1 to 3 of xsqrt(3x^2-2)

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

\frac{124}{9}

Decimal

13.77777 \dots

Solution steps

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

Apply u-substitution

: \int_{1}^{25} \frac{u}{6} d u

= \int_{1}^{25} \frac{u}{6} d u

Take the constant out:

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

= \frac{1}{6} \cdot \int_{1}^{25} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{25}

= \frac{1}{6} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{25}

Compute the boundaries:

\frac{248}{3}

= \frac{1}{6} \cdot \frac{248}{3}

Simplify

= \frac{124}{9}

\int_{0}^{\frac{π}{2}} x sin^{2} (\frac{x}{2}) d x

\int_{0}^{4 π} sin^{2} (x) d x

\int_{0}^{\infty} \frac{3}{x ^{2}} d x

\int_{1}^{\frac{π}{2}} cos (x) d x

\int_{2}^{\infty} \frac{3}{x ^{2}} d x

What is the integral from 1 to 3 of xsqrt(3x^2-2) ?
The integral from 1 to 3 of xsqrt(3x^2-2) is 124/9