1. The graph of f is given below. Using what you know about integrals, integral
ID: 2886701 • Letter: 1
Question
1. The graph of f is given below. Using what you know about integrals, integral properties, and methods for approximating the value of definite integrals, explain why the first three values are incorrect and the value in part (d) is correct for the value of / f(x)dx. Think about arguments that would convince your classmates. You may find it helpful to use areas of known geometric shapes to estimate the value of /f()dx Be sure to consider when you have an overestimate or underestimate. Note: Copies of the graph are provided with each response in case you would like to refer to or use the graph in your explanation (a) 1.78829. Explain why this response is incorrect. 0:04 b) 0.017883. Explain why this response is incorrect. 0-0 0:06Explanation / Answer
Integral of a function w.r.t. x will give us the area between it and x - axis. If the graph is above the x axis , value if integral will be positive otherwise it will be negative. Since the given graph is above x - axis, so the value of integral will be positive. So the option A is wrong.
If we draw a straight line from the starting point of the graph, which is (1,0), to the end point (4,.095) ,then the approximate area can be written as the area of triangle formed with (1,0), (4,0) and (4,.095) + small area between curved line and the drawn straight line. Which is approximately
(1/2)*(4-1)*.095 = .1425 + small area in-between
This is reasonbly close to the option D, option B is too large and option C is too small compared to the approx calculated value of integral. So both B and C can't be answer.
We can't know know the exact value since we don't know the function f(x) . So by approximation correct answer is D.
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