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

The integral from 0 to 2 of xsqrt(4x^2+9) is 49/6

Popular >

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

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

\frac{49}{6}

Decimal Notation

8.16666 \dots

Solution steps

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

Apply u-substitution

: \int_{9}^{25} \frac{u}{8} d u

= \int_{9}^{25} \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_{9}^{25} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{9}^{25}

= \frac{1}{8} [\frac{2}{3} u^{\frac{3}{2}}]_{9}^{25}

Compute the boundaries:

\frac{196}{3}

= \frac{1}{8} \cdot \frac{196}{3}

Simplify

= \frac{49}{6}

(e^{- \frac{x ^{2}}{2}})^{^{'}}

\int \frac{7}{1 - x ^{2}} d x

\frac{\partial}{\partial x} (35 x^{6} y^{4} - 24 x^{5} y^{3})

\frac{d y}{d t} - \frac{3}{t} y = 2 t^{3} e^{2 t}

\frac{d}{d x} (x^{3} + 2 x^{2} - 4 x + 2)

What is the integral from 0 to 2 of xsqrt(4x^2+9) ?
The integral from 0 to 2 of xsqrt(4x^2+9) is 49/6