The regions ( mathrm{A}, mathrm{B}, mathrm{C}, mathrm{D} ), and ( mathrm{E} ) in the figure below are bounded by the graph of the function ( f ) and the ( x )-axis. The areas of each enclosed region are labeled in the figure with their respective numerical values. What is the value of ( int_{-2}^{3}(f(x)+1) d x ? )

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Accepted Answer

Step:1 ：( int_{-2}^{3}(f(x)+1) d x = int_{-2}^{3}f(x) d x + int_{-2}^{3}1 d x )Step:2 ：( int_{-2}^{3}f(x) d x = (4+8+20)-(-1+2+15) = 9 )Step:3 ：( int_{-2}^{3}1 d x = 3 - (-2) = 5 )Step:4 ：( int_{-2}^{3}(f(x)+1) d x = 9 + 5 = 14 )

Answer

Step: 1 ：( int_{-2}^{3}(f(x)+1) d x = int_{-2}^{3}f(x) d x + int_{-2}^{3}1 d x )Step: 2 ：( int_{-2}^{3}f(x) d x = (4+8+20)-(-1+2+15) = 9 )Step: 3 ：( int_{-2}^{3}1 d x = 3 - (-2) = 5 )Step: 4 ：( int_{-2}^{3}(f(x)+1) d x = 9 + 5 = 14 )

The regions $A, B, C, D$ , and $E$ in the figure below are bounded by the graph of the function $f$ and the $x$ -axis. The areas of each enclosed region are labeled in the figure with their respective numerical values. What is the value of $\int_{- 2}^{3} (f (x) + 1) d x ?$

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The regions A,B,C,D, and E in the figure below are bounded by the graph of the function f and the x-axis. The areas of each enclosed region are labeled in the figure with their respective numerical values. What is the value of ∫−23(f(x)+1)dx?

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The regions $A, B, C, D$ , and $E$ in the figure below are bounded by the graph of the function $f$ and the $x$ -axis. The areas of each enclosed region are labeled in the figure with their respective numerical values. What is the value of $\int_{- 2}^{3} (f (x) + 1) d x ?$