Compute the area of the shaded region in two different ways: 

(a) By using simple geometric formulas; 

(b) By applying Theorem I.

Transcribed Image Text:

Theorem I: Area under a Graph If f(x) is a continuous nonnegative function on the interval a ≤ x ≤ b, then the area under the graph of f(x), above the x-axis, from x = a to x = b is equal to the definite integral of f from a to b: "]-[*Foode = a Area under the graph of f from x = a to x=b where F is an antiderivative of f (Fig. 4). f(x)dx= F(b) - F(a),