Problem

\( \int_{-2}^{4} x^{2} \operatorname{sgn}\left(9-x^{2}\right) d x \) ifadesinin değeri

Answer

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Answer

\( \left[\frac{x^3}{3}\right]_{-2}^3 - \left[\frac{x^3}{3}\right]_{3}^4 \)

Steps

Step 1 ：\( \operatorname{sgn}(9-x^2) = \begin{cases} 1, & x^2<9 \\ 0, & x^2=9 \\ -1, & x^2>9 \end{cases} \)

Step 2 ：\( \int_{-2}^{4} x^{2} \operatorname{sgn}\left(9-x^{2}\right) d x = \int_{-2}^{3} x^{2} d x - \int_{3}^{4} x^{2} d x \)

Step 3 ：\( \left[\frac{x^3}{3}\right]_{-2}^3 - \left[\frac{x^3}{3}\right]_{3}^4 \)

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