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

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

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

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

\frac{5 5}{3}

Decimal

3.72677 \dots

Solution steps

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

Apply u-substitution

= \int_{0}^{5} u^{2} d u

Apply the Power Rule

= [\frac{u ^{3}}{3}]_{0}^{5}

Compute the boundaries:

\frac{5 5}{3}

= \frac{5 5}{3}

\int_{0}^{1} - x^{3} d x

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

\int_{- 4}^{4} ∣ x - 2 ∣ d x

\int_{- 2}^{1} - x + 2 - x^{2} d x

\int_{0}^{5} (x - 3) (x - 1) d x

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