Directions: Solve each of the following problems, using available space for scra

Question

Directions: Solve each of the following problems, using available space for scratchwork. After examining the form of the choices, decide which is the best of the choices given. Do not spend too much time on any one problem. Calculators may be used on this part of the exam. In this test: (1) The exact numerical value of the correct answer does not always appear among the choices given. When this happens, select from among the choices, the number that best approximates the exact numerical value. (2) Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(z) is a real number. Let f be a continuous function such that integral^3_2 f(2x) dx = 8. What is the value of integral^6_4 f(x) dx? 4 8 12 16 32

Explanation / Answer

To understand this question, it is important to know the relation between graph of f(x) and graph of f(ax);
Graph of f(ax) is a times compressed along the x-axis (compressed sideways); Thus f(x) from x=0 to x=3 will be the same as f(3x) from 3x=0 to 3x=3/3=1

Thus f(2x) dx from x=2 to x=3 will be like f (x) dx from x=2*2 to x=3*2 which is from x=4 to x=6; Thus since the graph is the same (i.e. f(x) ) and period or interval is also same (i.e. x=4 x=6) the area covered , which is represented by the integral, will also be the same;Hence the answer is =8;

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