Find the area (in square units) of the region under the graph of the function f on the interval [3, 9].

Question

Find the area (in square units) of the region under the graph of the function f on the interval [3, 9].

f(x)=6e^x-x

Answer 1

f(x) = 6e^x - x is positive and continuous on the interval [3,9].

Area below the graph of f(x) and above the x-axis = ∫_{(from 3 to 9)} [6e^x - x]dx = [6e^x - (1/2)x²]_{(from 3 to 9)} =

(6e⁹ - 81/2) - (6e³ - 9/2) = 6(e⁹ - e³) - 36