What is the integral from 0 to 1 of xsqrt(10+4x^2) ?

The integral from 0 to 1 of xsqrt(10+4x^2) is (7sqrt(14)-5sqrt(10))/6

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integral from 0 to 1 of xsqrt(10+4x^2)

\int_{0}^{1} x 10 + 4 x^{2} d x

\frac{7 14 - 5 10}{6}

Decimal Notation

1.73003 \dots

Solution steps

\int_{0}^{1} x 10 + 4 x^{2} d x

Apply u-substitution

: \int_{10}^{14} \frac{u}{8} d u

= \int_{10}^{14} \frac{u}{8} d u

Take the constant out:

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

= \frac{1}{8} \cdot \int_{10}^{14} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{10}^{14}

= \frac{1}{8} [\frac{2}{3} u^{\frac{3}{2}}]_{10}^{14}

Compute the boundaries:

\frac{28 14 - 20 10}{3}

= \frac{1}{8} \cdot \frac{28 14 - 20 10}{3}

Simplify

= \frac{7 14 - 5 10}{6}

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\int_{0}^{1} - 2 t d t

What is the integral from 0 to 1 of xsqrt(10+4x^2) ?
The integral from 0 to 1 of xsqrt(10+4x^2) is (7sqrt(14)-5sqrt(10))/6