Find the Integral Below:

Question

Please show a graph and a step by step process of how to graph the piece wise function for the integral.

Answer 1

Between x = 0 and x = 6, the graph of f(x) is the horizontal line segment with endpoints (0,6) and (6,6).

Between x = 6 and x = 10, the graph of f(x) is the line segment with endpoints (6,6) and (10,10).

∫_{(0 to 10)} f(x)dx = area below the graph of f(x) and above the x-axis between x = 0 and x = 10.

= (area between x = 0 and x = 6) + (area between x = 6 and x = 10)

= (area of rectangle with length = width = 6) + (area of trapezoid with bases 6 and 10 and height 4)

= (6)(6) + (1/2)(6 + 10)(4) = 36 + 32 = 68