What is the integral from 1 to 2 of 3xsqrt(x^2-1) ?

The integral from 1 to 2 of 3xsqrt(x^2-1) is 3sqrt(3)

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integral from 1 to 2 of 3xsqrt(x^2-1)

\int_{1}^{2} 3 x x^{2} - 1 d x

33

Solution steps

\int_{1}^{2} 3 x x^{2} - 1 d x

Take the constant out:

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

= 3 \cdot \int_{1}^{2} x x^{2} - 1 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:

3

= 33

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What is the integral from 1 to 2 of 3xsqrt(x^2-1) ?
The integral from 1 to 2 of 3xsqrt(x^2-1) is 3sqrt(3)