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Question: Evaluate :\(\int _ { - 1 } ^ { 1 }\)max {2 – x, 2, 1 + x} dx. -...

Evaluate :∫−11\int _ { - 1 } ^ { 1 }max {2 – x, 2, 1 + x} dx. -

A

B

C

103\frac { 10 } { 3 }

D

94\frac { 9 } { 4 }

Answer

Explanation

Solution

The graph of ƒ(x) = max {2 – x, 2, 1 + x} is shown as in figure

Therefore ∫−11\int _ { - 1 } ^ { 1 } max {2 – x, 2, 1 + x} dx = Area of shaded region

= 12\frac { 1 } { 2 } (2 + 3) × 1 + 1 × 2

= 92\frac { 9 } { 2 }