Find
4 f(x) dx 0
if f(x) =
.
2 for x < 2 x for x ≥ 2
How should I go about starting this type of problem. I'm not sure what deltax would be since they dont give an "n" value.
What "n" or "deltax" are you talking about? Does this problem specifically require you to use a "Riemann sum" approximation?
It should be easy to find the exact value "geometrically". For x= 0 to 2, the graph is a horizontal straight line, y= 2, so the "area under the curve" is the area of a square, 2 high and 2 wide. For x= 2 to 4, the graph is a straight line through (2, 2) and (4, 4). The area under that is the area of a trapezoid with "height" 2 (x= 2 to x= 4) and bases of length 2 (y= 0 to y= 2) and 4 (y= 0 to y= 4). If you don't want to use the formula for area of a trapezoid, note that drawing a horizontal line from (2, 2) to (4,2) divides that trapezoid into a 2 by 2 square and a right triangle with base of length 2 and height 2.