What is the integral from 0 to 2 of sqrt(144x+289) ?

The integral from 0 to 2 of sqrt(144x+289) is (577sqrt(577)-4913)/(216)

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integral from 0 to 2 of sqrt(144x+289)

\int_{0}^{2} 144 x + 289 d x

\frac{577 577 - 4913}{216}

Decimal

41.42136 \dots

Solution steps

\int_{0}^{2} 144 x + 289 d x

Apply u-substitution

: \int_{289}^{577} \frac{u}{144} d u

= \int_{289}^{577} \frac{u}{144} d u

Take the constant out:

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

= \frac{1}{144} \cdot \int_{289}^{577} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{289}^{577}

= \frac{1}{144} [\frac{2}{3} u^{\frac{3}{2}}]_{289}^{577}

Compute the boundaries:

\frac{1154 577}{3} - \frac{9826}{3}

= \frac{1}{144} (\frac{1154 577}{3} - \frac{9826}{3})

Simplify

= \frac{577 577 - 4913}{216}

16 4 4 x^{4} + 4

t^{3} - \frac{1}{4 t ^{7}}

\frac{\partial}{\partial y} (y^{2} sin (x))

f (x) = \frac{1}{x - 1}, at x = 2

\frac{1}{s ( s + 8 )}

What is the integral from 0 to 2 of sqrt(144x+289) ?
The integral from 0 to 2 of sqrt(144x+289) is (577sqrt(577)-4913)/(216)