What is the integral from 0 to 2 of sqrt(36x+145) ?

The integral from 0 to 2 of sqrt(36x+145) is (217sqrt(217)-145sqrt(145))/(54)

integral from 0 to 2 of sqrt(36x+145)

\int_{0}^{2} 36 x + 145 d x

\frac{217 217 - 145 145}{54}

Decimal

26.86256 \dots

Solution steps

\int_{0}^{2} 36 x + 145 d x

Apply u-substitution

= \int_{145}^{217} \frac{u}{36} d u

Take the constant out:

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

= \frac{1}{36} \cdot \int_{145}^{217} u d u

Apply the Power Rule

= \frac{1}{36} [\frac{2}{3} u^{\frac{3}{2}}]_{145}^{217}

Compute the boundaries:

\frac{434 217 - 290 145}{3}

= \frac{1}{36} \cdot \frac{434 217 - 290 145}{3}

Simplify

= \frac{217 217 - 145 145}{54}

l a pl a ce t r an s f or m t^{2} + 6 t - 17

\frac{\partial}{\partial x} (- \frac{x}{( x + y ) ^{2}})

\int_{0}^{+ oo} x \cdot (x + 1)^{- 2} d x

f (x) = 5 - x

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

What is the integral from 0 to 2 of sqrt(36x+145) ?
The integral from 0 to 2 of sqrt(36x+145) is (217sqrt(217)-145sqrt(145))/(54)