What is the integral from-5 to-3 of sqrt(x^2-4) ?

The integral from-5 to-3 of sqrt(x^2-4) is

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integral from-5 to-3 of sqrt(x^2-4)

\int_{- 5}^{- 3} x^{2} - 4 d x

4 \frac{1}{8} (- 3) (- 3)^{2} - 4 - \frac{1}{2} ln \frac{- 3 + ( - 3 ) ^{2} - 4}{2} - 4 \frac{1}{8} (- 5) (- 5)^{2} - 4 - \frac{1}{2} ln \frac{- 5 + ( - 5 ) ^{2} - 4}{2}

Decimal

6.89358 \dots

Solution steps

\int_{- 5}^{- 3} x^{2} - 4 d x

Compute the indefinite integral:

\int x^{2} - 4 d x = 4 (\frac{1}{8} x x^{2} - 4 - \frac{1}{2} ln (\frac{x + x ^{2} - 4}{2})) + C

Compute the boundaries:

\int_{- 5}^{- 3} x^{2} - 4 d x = 4 \frac{1}{8} (- 3) (- 3)^{2} - 4 - \frac{1}{2} ln \frac{- 3 + ( - 3 ) ^{2} - 4}{2} - 4 \frac{1}{8} (- 5) (- 5)^{2} - 4 - \frac{1}{2} ln \frac{- 5 + ( - 5 ) ^{2} - 4}{2}

= 4 \frac{1}{8} (- 3) (- 3)^{2} - 4 - \frac{1}{2} ln \frac{- 3 + ( - 3 ) ^{2} - 4}{2} - 4 \frac{1}{8} (- 5) (- 5)^{2} - 4 - \frac{1}{2} ln \frac{- 5 + ( - 5 ) ^{2} - 4}{2}

What is the integral from-5 to-3 of sqrt(x^2-4) ?
The integral from-5 to-3 of sqrt(x^2-4) is