The graph of g(x) consists of two straight lines and a semicircle. Use it to evaluate the integral. 8 y = g(x) 4 0 8 14 Exercise (a) "9( x ) dx Part 1 of 2 If g(x) is positive, then the integral g(x) dx corresponds to the area beneath g(x) and above the x-axis over the interval [a, b]. On [0, 4], the function g(x) is above the x-axis and is therefore positive. Thus, g(x) dx equals the area of the triangle created by the function, the x-axis, and the y-axis. This triangle is a right triangle with a side length of 4 4 along the x-axis and a side length of 8 8 along the y-axis. (Give the numeric values.) Part 2 of 2 Since the area of a triangle with base b and height h is A = , then our triangle has an area of Thus , 69( * ) dx = Submit Skip (you cannot come back). Exercise (b) " 9( * ) dx Part 1 of 3 On the interval [4, 12], the graph is a semi-circle. Since the semi-circle is below the x-axis, then g(x) dx is the negative of the area of this semi-circle. The radius of this semi-circle is r = 4 | 4 Part 2 of 3 A circle of radius r has an area A , and so our semi-circle has an area A = Submit Skip (you cannot come back) Exercise (c) ["( x ) dx Part 1 of 2 On the interval [12, 14], the graph again forms a triangle above the x-axis. Therefore, g(x) dx equals the area of this triangle, which is (2 - 2 )(2 | 2 )- 2 v 2. Part 2 of 2 Submit Skip ( you cannot come back ) Tutorial Exercise If /2 ((x ) dx = 9 and ( 1(x ) dx = 4.8 , find ( "(( x ) dx . Part 1 of 3 We know that for a s b s c, Since we have 2 s 4 s 6. "F(x) dx + ( F(x) dx - f (x) dx. P 2 Part 2 of 3 Therefore, ( x ) dx . Submit Skip_(you cannot come back)