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

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

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

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

2 (\frac{8}{3} - 3)

Decimal

1.86923 \dots

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

Apply the Power Rule

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

Compute the boundaries:

\frac{8}{3} - 3

= 2 (\frac{8}{3} - 3)

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