What is the integral from 0 to 1 of xsqrt(75x^2+25) ?

The integral from 0 to 1 of xsqrt(75x^2+25) is 35/9

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integral from 0 to 1 of xsqrt(75x^2+25)

\int_{0}^{1} x 75 x^{2} + 25 d x

\frac{35}{9}

Solution steps

\int_{0}^{1} x 75 x^{2} + 25 d x

Apply u-substitution

: \int_{25}^{100} \frac{u}{150} d u

= \int_{25}^{100} \frac{u}{150} d u

Take the constant out:

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

= \frac{1}{150} \cdot \int_{25}^{100} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{25}^{100}

= \frac{1}{150} [\frac{2}{3} u^{\frac{3}{2}}]_{25}^{100}

Compute the boundaries:

\frac{1750}{3}

= \frac{1}{150} \cdot \frac{1750}{3}

Simplify

= \frac{35}{9}

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What is the integral from 0 to 1 of xsqrt(75x^2+25) ?
The integral from 0 to 1 of xsqrt(75x^2+25) is 35/9