What is the integral from-2 to 5 of (|9-x^2|-x^2) ?

The integral from-2 to 5 of (|9-x^2|-x^2) is 11/3

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integral from-2 to 5 of (|9-x^2|-x^2)

\int_{- 2}^{5} (9 - x^{2} - x^{2}) d x

\frac{11}{3}

Decimal

3.66666 \dots

Solution steps

\int_{- 2}^{5} 9 - x^{2} - x^{2} d x

Eliminate Absolutes

= \int_{- 2}^{3} 9 - x^{2} - x^{2} d x + \int_{3}^{5} - 9 + x^{2} - x^{2} d x

\int_{- 2}^{3} 9 - x^{2} - x^{2} d x = \frac{65}{3}

\int_{3}^{5} - 9 + x^{2} - x^{2} d x = - 18

= \frac{65}{3} - 18

Simplify

\frac{65}{3} - 18 : \frac{11}{3}

= \frac{11}{3}

\int_{0}^{1} x^{\frac{2}{9}} d x

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\int_{0}^{1} x \frac{3}{2} (1 - x^{2}) d x

\int_{0}^{3} π 4 x + 5 d x

\int_{0}^{1} \frac{x}{1 + 3 x + 1} d x

What is the integral from-2 to 5 of (|9-x^2|-x^2) ?
The integral from-2 to 5 of (|9-x^2|-x^2) is 11/3