Find the total area between the gurve and the given interval

[hank]

on the x-axis for:
\(\displaystyle \begin{array}{l}
y = e^x - 1 \\

\smallint _{ - 1}^1 e^x - 1 \\
= e^x - x|_{ - 1}^1 \\
= e - 1 - e^{ - 1} - 1 \\
= e - e^{ - 1} + 2 \\
= e + e^{ - 1} + 2 \\
\end{array}\)
Ok, the first line is what I'm supposed to find the area for.
Lines 2 thru 4 are my work. The answer is line 5. However, according to the book, the answer is line 6.

Can someone show me where I went wrong, or is the book wrong?

Thanks in advance..

 

[galactus]

Re: Find the total area between the gurve and the given inte

on the x-axis for:
\(\displaystyle \begin{array}{l}
y = e^x - 1 \\

{ - 1}^1 e^x - 1 \\
= e^x - x|_{ - 1}^1 \\
=\underbrace{e - 1 - e^{ - 1} - 1}_{\text{\downarrow}}\\
=e-\frac{1}{e}-2\leftarrow\text{correct answer}
\end{array}\)
Ok, the first line is what I'm supposed to find the area for.
Lines 2 thru 4 are my work. The answer is line 5. However, according to the book, the answer is line 6.

Can someone show me where I went wrong, or is the book wrong?

Thanks in advance..