What is the integral from 0 to 1 of xsqrt(x^2+3) ?

The integral from 0 to 1 of xsqrt(x^2+3) is 8/3-sqrt(3)

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integral from 0 to 1 of xsqrt(x^2+3)

\int_{0}^{1} x x^{2} + 3 d x

\frac{8}{3} - 3

Decimal

0.93461 \dots

Solution steps

\int_{0}^{1} x x^{2} + 3 d x

Apply u-substitution

= \int_{3}^{2} u^{2} d u

Apply the Power Rule

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

Compute the boundaries:

\frac{8}{3} - 3

= \frac{8}{3} - 3

What is the integral from 0 to 1 of xsqrt(x^2+3) ?
The integral from 0 to 1 of xsqrt(x^2+3) is 8/3-sqrt(3)