What is the integral from 30 to 200 of sqrt(50x-30) ?

The integral from 30 to 200 of sqrt(50x-30) is (2(997sqrt(9970)-1029sqrt(30)))/(15)

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integral from 30 to 200 of sqrt(50x-30)

\int_{30}^{200} 50 x - 30 d x

\frac{2 ( 997 9970 - 1029 30 )}{15}

Decimal Notation

12521.90300 \dots

Solution steps

\int_{30}^{200} 50 x - 30 d x

Apply u-substitution

: \int_{1470}^{9970} \frac{u}{50} d u

= \int_{1470}^{9970} \frac{u}{50} d u

Take the constant out:

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

= \frac{1}{50} \cdot \int_{1470}^{9970} u d u

Apply the Power Rule

: [\frac{2}{3} u^{\frac{3}{2}}]_{1470}^{9970}

= \frac{1}{50} [\frac{2}{3} u^{\frac{3}{2}}]_{1470}^{9970}

Compute the boundaries:

\frac{19940 9970}{3} - 686030

= \frac{1}{50} (\frac{19940 9970}{3} - 686030)

Simplify

= \frac{2 ( 997 9970 - 1029 30 )}{15}

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What is the integral from 30 to 200 of sqrt(50x-30) ?
The integral from 30 to 200 of sqrt(50x-30) is (2(997sqrt(9970)-1029sqrt(30)))/(15)