Find the integral ∫_(−3) ^3 { ((x^3 −x),((x≤0))),(x^2 ,((x≥0))) :}dx


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Question Number 199471 by MathematicalUser2357 last updated on 04/Nov/23
$Find the integral ∫_(−3) ^3 { ((x^3 −x),((x≤0))),(x^2 ,((x≥0))) :}dx$
$F i n d t h e i n t e g r a l$ $\int_{- 3}^{3} {\begin{cases} x^{3} - x & (x \leq 0) \\ x^{2} & (x \geq 0) \end{cases} d x$
	Answered by Frix last updated on 04/Nov/23

	$\underset{a}{\int^{b}} f (x) d x = \underset{a}{\int^{c}} f (x) d x + \underset{c}{\int^{b}} f (x) d x$ $\underset{- 3}{\int^{0}} (x^{3} - x) d x + \underset{0}{\int^{3}} x^{2} d x = - \frac{27}{4}$
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