What is the integral from 2 to 9 of 3xsqrt(x^2-1) ?

The integral from 2 to 9 of 3xsqrt(x^2-1) is 320sqrt(5)-3sqrt(3)

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integral from 2 to 9 of 3xsqrt(x^2-1)

\int_{2}^{9} 3 x x^{2} - 1 d x

3205 - 33

Decimal

710.34560 \dots

Solution steps

\int_{2}^{9} 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_{2}^{9} x x^{2} - 1 d x

Apply u-substitution

: \int_{3}^{45} u^{2} d u

= 3 \cdot \int_{3}^{45} u^{2} d u

Apply the Power Rule

: [\frac{u ^{3}}{3}]_{3}^{45}

= 3 [\frac{u ^{3}}{3}]_{3}^{45}

Compute the boundaries:

\frac{320 5}{3} - 3

= 3 (\frac{320 5}{3} - 3)

Simplify

= 3205 - 33

\int_{0}^{1} x^{11} d x

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\int_{0}^{2} 9 x^{2} e^{x^{3}} d x

\int_{1}^{4} (\frac{1}{x} + x) d x

\int_{- 1}^{1} \frac{y ^{3}}{3} + 2 y^{3} d y

What is the integral from 2 to 9 of 3xsqrt(x^2-1) ?
The integral from 2 to 9 of 3xsqrt(x^2-1) is 320sqrt(5)-3sqrt(3)