What is the integral from 0 to 6 of 15sqrt(4x+1) ?

The integral from 0 to 6 of 15sqrt(4x+1) is 310

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integral from 0 to 6 of 15sqrt(4x+1)

\int_{0}^{6} 15 4 x + 1 d x

310

Solution steps

\int_{0}^{6} 15 4 x + 1 d x

Take the constant out:

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

= 15 \cdot \int_{0}^{6} 4 x + 1 d x

Apply u-substitution

: \int_{1}^{25} \frac{u}{4} d u

= 15 \cdot \int_{1}^{25} \frac{u}{4} d u

Take the constant out:

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

= 15 \cdot \frac{1}{4} \cdot \int_{1}^{25} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{25}

= 15 \cdot \frac{1}{4} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{25}

Simplify

15 \cdot \frac{1}{4} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{25} : \frac{15}{4} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{25}

= \frac{15}{4} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{25}

Compute the boundaries:

\frac{248}{3}

= \frac{15}{4} \cdot \frac{248}{3}

Simplify

= 310

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What is the integral from 0 to 6 of 15sqrt(4x+1) ?
The integral from 0 to 6 of 15sqrt(4x+1) is 310