Calculate the area of the figure bounded by lines y = e ^ x; y = 1; x = 2

Find the point of intersection of the graphs of the functions y = e ^ x and y = 1, for this we equate the equations to each other:

e ^ x = 1;

ln (e ^ x) = ln (1);

x = 0.

Then the area S of the figure formed by the given lines is equal to:

S = ∫e ^ x * dx | 0; 2 = e ^ x | 0; 2 = e ^ 2 – e ^ 0 = e ^ 2 – 1.

Answer: the required area is e ^ 2 – 1.