in Calculus
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$\int_{-3}^{3} \left | X+1 \right |dx$
in Calculus
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Best answer

First we need to define the function piecewise :

f(x)   =  -(x + 1)  , if x < -1

        =  x + 1 , otherwise

So given integral simplifies to :

=  ( x2 / 2  + x ) |3-1      -  ( x2 / 2  + x ) | -1-3

=  (9/2 + 3  - 1/2 + 1)  - ( 1/2 - 1 - 9/2 + 3 ) 

=  (4 + 3 + 1)  - ( - 4 - 1 + 3 )

=  8 + 2

=  10

Hence the given integral evaluates to 10

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$\begin{align*}
&= \int_{-3}^{+3} |x+1| dx \\
&= \int_{-2}^{+4} |y| dy \\
&= \frac{2 \cdot 2}{2} + \frac{4 \cdot 4}{2} \qquad \left [\text{ directly from graph structure}  \right ]  \\
&= 10 \\
\end{align*}$
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