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

The integral from 0 to 2 of xsqrt(1+x^2) is (5sqrt(5)-1)/3

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

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

\frac{5 5 - 1}{3}

Decimal

3.39344 \dots

Solution steps

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

Apply u-substitution

= \int_{1}^{5} u^{2} d u

Apply the Power Rule

= [\frac{u ^{3}}{3}]_{1}^{5}

Compute the boundaries:

\frac{5 5}{3} - \frac{1}{3}

= \frac{5 5}{3} - \frac{1}{3}

Simplify

= \frac{5 5 - 1}{3}

What is the integral from 0 to 2 of xsqrt(1+x^2) ?
The integral from 0 to 2 of xsqrt(1+x^2) is (5sqrt(5)-1)/3