Sketch the graph and find the area of the region bounded by the graph of the function f and lines y = 0, x = a and x = b.

Question

Quizplus · Accepted Answer

The graph of the function f will be a positive, decreasing exponential function with the x-axis as its horizontal asymptote. 
The area of the region bounded by the graph of the function f and lines y = 0, x = a and x = b is given by the integral:

∫(0 to ∞) f(x) dx - ∫(0 to a) f(x) dx - ∫(b to ∞) f(x) dx

Since the function f is positive and decreasing, the first integral converges to a finite value. The second and third integrals are also finite since they are integrals of bounded functions. Therefore, the area of the region is a finite value.

Option C is the only option that gives a finite value in the answer choices.

Sketch the Graph and Find the Area of the Region