What is the integral from-2 to-1 of 2x(7-x^2)^3 ?

The integral from-2 to-1 of 2x(7-x^2)^3 is -1215/4

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integral from-2 to-1 of 2x(7-x^2)^3

\int_{- 2}^{- 1} 2 x (7 - x^{2})^{3} d x

- \frac{1215}{4}

Decimal

- 303.75

Solution steps

\int_{- 2}^{- 1} 2 x (7 - x^{2})^{3} d x

Take the constant out:

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

= 2 \cdot \int_{- 2}^{- 1} x (7 - x^{2})^{3} d x

Apply u-substitution

: \int_{3}^{6} - \frac{u ^{3}}{2} d u

= 2 \cdot \int_{3}^{6} - \frac{u ^{3}}{2} d u

Take the constant out:

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

= 2 (- \frac{1}{2} \cdot \int_{3}^{6} u^{3} d u)

Apply the Power Rule

: [\frac{u ^{4}}{4}]_{3}^{6}

= 2 (- \frac{1}{2} [\frac{u ^{4}}{4}]_{3}^{6})

Simplify

2 (- \frac{1}{2} [\frac{u ^{4}}{4}]_{3}^{6}) : - [\frac{u ^{4}}{4}]_{3}^{6}

= - [\frac{u ^{4}}{4}]_{3}^{6}

Compute the boundaries:

\frac{1215}{4}

= - \frac{1215}{4}

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What is the integral from-2 to-1 of 2x(7-x^2)^3 ?
The integral from-2 to-1 of 2x(7-x^2)^3 is -1215/4