Answer to Question #117681 in Calculus for Lizwi

Question

Find the area of the region enclosed enclosed between the graphs of y=e^x and y=e^-x and the line x=ln2.

Answer 1

$Area=\int_{ln(2)}^1(-ln(y)-ln(y))dy\\ \ \qquad \ = -2\int_{ln(2)}^1ln(y)dy\\ \ \qquad \ = -2y (ln(y)-1)|_{ln(2)}^1\\ \ \qquad \ = -2(ln(1)-1)+2ln(2)(ln(ln(2))-1)\\ \ \qquad \ = 2+2ln(2)(ln(ln(2))-1)\\$