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

Question

Accepted Answer

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 )

Answer

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 )

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

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