What is the integral from 0 to 1 of xsqrt(91x^2+9) ?

The integral from 0 to 1 of xsqrt(91x^2+9) is 139/39

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integral from 0 to 1 of xsqrt(91x^2+9)

\int_{0}^{1} x 91 x^{2} + 9 d x

\frac{139}{39}

Decimal

3.56410 \dots

Solution steps

\int_{0}^{1} x 91 x^{2} + 9 d x

Apply u-substitution

: \int_{9}^{100} \frac{u}{182} d u

= \int_{9}^{100} \frac{u}{182} d u

Take the constant out:

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

= \frac{1}{182} \cdot \int_{9}^{100} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{9}^{100}

= \frac{1}{182} [\frac{2}{3} u^{\frac{3}{2}}]_{9}^{100}

Compute the boundaries:

\frac{1946}{3}

= \frac{1}{182} \cdot \frac{1946}{3}

Simplify

= \frac{139}{39}

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What is the integral from 0 to 1 of xsqrt(91x^2+9) ?
The integral from 0 to 1 of xsqrt(91x^2+9) is 139/39