If f(x)= { ((2x ; 0<x<1)),((3 ; x=1 )),((6x−1 ; 1<x<2)) :} find ∫


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Question Number 124794 by benjo_mathlover last updated on 06/Dec/20
$If f(x)= { ((2x ; 0<x<1)),((3 ; x=1 )),((6x−1 ; 1<x<2)) :} find ∫_0 ^2 f(x) dx ?$
$I f f (x) = {\begin{cases} 2 x; 0 < x < 1 \\ 3; x = 1 \\ 6 x - 1; 1 < x < 2 \end{cases}$ $f i n d \underset{0}{\int^{2}} f (x) d x ?$
	Answered by TITA last updated on 06/Dec/20

	$\int_{0}^{2} f (x) d x = 2 \int_{0}^{1} x d x + 3 + \int_{1}^{2} (6 x - 1) d x l e t \int_{0}^{2} f (x) d x = I$ $\Rightarrow I = x^{2} ∣_{0}^{1} + 3 + {(3 x^{2} - x)}_{1}^{2}$ $I = 4 + (10 - 2) = - 4 p l e a s e c h e c k g u y s$
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