What is the integral from-14 to 1 of x|49-x^2| ?

The integral from-14 to 1 of x|49-x^2| is -23913/4

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integral from-14 to 1 of x|49-x^2|

\int_{- 14}^{1} x 49 - x^{2} d x

- \frac{23913}{4}

Decimal

- 5978.25

Solution steps

\int_{- 14}^{1} x 49 - x^{2} d x

Eliminate Absolutes

= \int_{- 14}^{- 7} x (- 49 + x^{2}) d x + \int_{- 7}^{1} x (49 - x^{2}) d x

\int_{- 14}^{- 7} x (- 49 + x^{2}) d x = - \frac{21609}{4}

\int_{- 7}^{1} x (49 - x^{2}) d x = - 576

= - \frac{21609}{4} - 576

Simplify

- \frac{21609}{4} - 576 : - \frac{23913}{4}

= - \frac{23913}{4}

What is the integral from-14 to 1 of x|49-x^2| ?
The integral from-14 to 1 of x|49-x^2| is -23913/4