What is the integral from 0 to 7 of (2xsqrt(x^2-1)) ?

The integral from 0 to 7 of (2xsqrt(x^2-1)) is 128sqrt(3)+i 2/3

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integral from 0 to 7 of (2xsqrt(x^2-1))

\int_{0}^{7} (2 x x^{2} - 1) d x

1283 + i \frac{2}{3}

Solution steps

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

Take the constant out:

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

= 2 \cdot \int_{0}^{7} x x^{2} - 1 d x

Apply u-substitution

: \int_{i}^{43} u^{2} d u

= 2 \cdot \int_{i}^{43} u^{2} d u

Apply the Power Rule

: [\frac{u ^{3}}{3}]_{i}^{43}

= 2 [\frac{u ^{3}}{3}]_{i}^{43}

Compute the boundaries:

643 + \frac{i}{3}

= 2 (643 + \frac{i}{3})

Simplify

= 1283 + i \frac{2}{3}

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What is the integral from 0 to 7 of (2xsqrt(x^2-1)) ?
The integral from 0 to 7 of (2xsqrt(x^2-1)) is 128sqrt(3)+i 2/3