What is the integral from 1 to 2 of sqrt(1+(9x)/4) ?

The integral from 1 to 2 of sqrt(1+(9x)/4) is (44sqrt(11)-13sqrt(26))/(27sqrt(2))

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integral from 1 to 2 of sqrt(1+(9x)/4)

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

\frac{44 11 - 13 26}{27 2}

Decimal

2.08581 \dots

Solution steps

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

Apply u-substitution

: \int_{\frac{13}{4}}^{\frac{11}{2}} \frac{4 u}{9} d u

= \int_{\frac{13}{4}}^{\frac{11}{2}} \frac{4 u}{9} d u

Take the constant out:

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

= \frac{4}{9} \cdot \int_{\frac{13}{4}}^{\frac{11}{2}} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{\frac{13}{4}}^{\frac{11}{2}}

= \frac{4}{9} [\frac{2}{3} u^{\frac{3}{2}}]_{\frac{13}{4}}^{\frac{11}{2}}

Compute the boundaries:

\frac{11 11}{3 2} - \frac{13 13}{12}

= \frac{4}{9} (\frac{11 11}{3 2} - \frac{13 13}{12})

Simplify

= \frac{44 11 - 13 26}{27 2}

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What is the integral from 1 to 2 of sqrt(1+(9x)/4) ?
The integral from 1 to 2 of sqrt(1+(9x)/4) is (44sqrt(11)-13sqrt(26))/(27sqrt(2))