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

The integral from 4 to 1 of xsqrt(x^2+4) is -(35sqrt(5))/3

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

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

- \frac{35 5}{3}

Decimal

- 26.08745 \dots

Solution steps

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

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

= - \int_{1}^{4} x x^{2} + 4 d x

Apply u-substitution

: \int_{5}^{25} u^{2} d u

= - \int_{5}^{25} u^{2} d u

Apply the Power Rule

: [\frac{u ^{3}}{3}]_{5}^{25}

= - [\frac{u ^{3}}{3}]_{5}^{25}

Compute the boundaries:

\frac{35 5}{3}

= - \frac{35 5}{3}

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What is the integral from 4 to 1 of xsqrt(x^2+4) ?
The integral from 4 to 1 of xsqrt(x^2+4) is -(35sqrt(5))/3