Does $\int _ { 1 } ^ { 3 } \left( e ^ { x } - 1 \right) d x$

question 50

Multiple Choice

Does $\int _ { 1 } ^ { 3 } \left( e ^ { x } - 1 \right) d x$ express the area between the curve y = $e ^ { x }$ - 1 and the x-axis between x = 1 and $x = 3 ?$ Give a reason for your answer.

• A) Yes, because y = \(e ^ { x }\) - 1 does not cross the x-axis between 1 and 3 .
• B) Yes, because y = \(e ^ { x }\) - 1 is nonnegative for all x between 1 and 3 .
• C) No, because \(\int _ { 1 } ^ { 3 } \left( e ^ { x } - 1 \right) d x\) is negative.
• D) No, because y = \(e ^ { x }\) - 1 crosses the x-axis between 1 and 3 .
• E) none of these

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