Question

The area bounded by the curve $y=e^x$ and the lines $y=|x-1|,x=2$ is given by:

• A. $e^2+1$
• B. $e^2-1$
• C. $e^2-2$
• D. $e-2$.

Answer 1

Answer: (C)

$e^2-2$

As you can see from the figure,

Area$={\int }_0^2(e^x-|x-1|)dx={\int }_0^2{e}^{x}dx-{\int }_0^1(1-x)dx-{\int }_1^2(x-1)dx$

$=e^x{|}_0^2+\frac{1}{2}\left(\right(1-x{)}^2{|}_0^1{-(x-1)}^2{|}_1^2)=(e^2-1)-\frac{1}{2}(1+1)=e^2-2$

So, Option C is the correct answer