What is the integral from 0 to 2 of sqrt(7x+1) ?

The integral from 0 to 2 of sqrt(7x+1) is (30sqrt(15)-2)/(21)

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integral from 0 to 2 of sqrt(7x+1)

\int_{0}^{2} 7 x + 1 d x

\frac{30 15 - 2}{21}

Solution steps

\int_{0}^{2} 7 x + 1 d x

Apply u-substitution

: \int_{1}^{15} \frac{u}{7} d u

= \int_{1}^{15} \frac{u}{7} d u

Take the constant out:

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

= \frac{1}{7} \cdot \int_{1}^{15} u d u

Apply the Power Rule

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

= \frac{1}{7} [\frac{2}{3} u^{\frac{3}{2}}]_{1}^{15}

Compute the boundaries:

1015 - \frac{2}{3}

= \frac{1}{7} (1015 - \frac{2}{3})

Simplify

= \frac{30 15 - 2}{21}

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What is the integral from 0 to 2 of sqrt(7x+1) ?
The integral from 0 to 2 of sqrt(7x+1) is (30sqrt(15)-2)/(21)