What is the integral from 0 to 1 of xsqrt(4+9x^2) ?

The integral from 0 to 1 of xsqrt(4+9x^2) is (13sqrt(13)-8)/(27)

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integral from 0 to 1 of xsqrt(4+9x^2)

\int_{0}^{1} x 4 + 9 x^{2} d x

\frac{13 13 - 8}{27}

Decimal Notation

1.43970 \dots

Solution steps

\int_{0}^{1} x 4 + 9 x^{2} d x

Apply u-substitution

: \int_{4}^{13} \frac{u}{18} d u

= \int_{4}^{13} \frac{u}{18} d u

Take the constant out:

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

= \frac{1}{18} \cdot \int_{4}^{13} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{4}^{13}

= \frac{1}{18} [\frac{2}{3} u^{\frac{3}{2}}]_{4}^{13}

Compute the boundaries:

\frac{26 13}{3} - \frac{16}{3}

= \frac{1}{18} (\frac{26 13}{3} - \frac{16}{3})

Simplify

= \frac{13 13 - 8}{27}

\int e^{2 x} \cdot sin (e^{x}) d x

\frac{\partial}{\partial x} (\frac{5 x yz}{x ^{2} + y ^{2} + z ^{2}})

y^{^{'}} + 2 y = 10 sin (t)

f (x) = 3 x^{2} + 5

\frac{\partial}{\partial t} (cos (3 t))

What is the integral from 0 to 1 of xsqrt(4+9x^2) ?
The integral from 0 to 1 of xsqrt(4+9x^2) is (13sqrt(13)-8)/(27)