Use this graph of f consisting of a quarter circle and two line segments.

Question

Use this graph of f consisting of a quarter circle and two line segments.

Based on the graph, 

20 + π.

20 + 4π.

40 + π.

40 + 4π.

Answer 1

40 + 4π.

4π from 1/4 area circle r=4

20 from the box 2 by 10

16 from box 4 by 4

4 from triangle base 2, height 4

Answer 2

The graph you provided is too small to see the scale on the y-axis, but all you have to do here is calculate the area below the graph of f(x) and above the x-axis. You can do this with area formulas from geometry: divide the region in to a rectangle of width 10 and height 2, a quarter circle with radius = 2, and the trapezoid of height 2 with bases = 6 and 4. Those measures unfortunately give a total area of 30 + π , which isn't among the answers listed. But again, difficult to see the y-scale on the provided graph.