What is the integral from 4 to 5 of 3xsqrt(x^2-16) ?

The integral from 4 to 5 of 3xsqrt(x^2-16) is 27

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integral from 4 to 5 of 3xsqrt(x^2-16)

\int_{4}^{5} 3 x x^{2} - 16 d x

27

Solution steps

\int_{4}^{5} 3 x x^{2} - 16 d x

Take the constant out:

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

= 3 \cdot \int_{4}^{5} x x^{2} - 16 d x

Apply u-substitution

: \int_{0}^{3} u^{2} d u

= 3 \cdot \int_{0}^{3} u^{2} d u

Apply the Power Rule

: [\frac{u ^{3}}{3}]_{0}^{3}

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

Compute the boundaries:

9

= 3 \cdot 9

Simplify

= 27

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What is the integral from 4 to 5 of 3xsqrt(x^2-16) ?
The integral from 4 to 5 of 3xsqrt(x^2-16) is 27