What is the integral from 4 to 12 of xsqrt(1+x^2) ?

The integral from 4 to 12 of xsqrt(1+x^2) is (145sqrt(145)-17sqrt(17))/3

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integral from 4 to 12 of xsqrt(1+x^2)

\int_{4}^{12} x 1 + x^{2} d x

\frac{145 145 - 17 17}{3}

Decimal

558.64613 \dots

Solution steps

\int_{4}^{12} x 1 + x^{2} d x

Apply u-substitution

: \int_{17}^{145} u^{2} d u

= \int_{17}^{145} u^{2} d u

Apply the Power Rule

: [\frac{u ^{3}}{3}]_{17}^{145}

= [\frac{u ^{3}}{3}]_{17}^{145}

Compute the boundaries:

\frac{145 145 - 17 17}{3}

= \frac{145 145 - 17 17}{3}

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What is the integral from 4 to 12 of xsqrt(1+x^2) ?
The integral from 4 to 12 of xsqrt(1+x^2) is (145sqrt(145)-17sqrt(17))/3