2. Evaluate the integrals using area formulas: (a) (b) 10 9-(x-7)² dx (10-2 (10-2|x) dx

Problems: 1. Engineers have observed that when transferring a message I (an input signal) through a physical medium some information is lost in the message O that is received (an output signal). Information may be lost due to dissipation as heat is transferred, or for other reasons, depending on physical context. For example, when we record music we do not record everything but a finite amount of information. If we represent the input signal by a function I(x), defined for x E [-1, 7], then one way to measure how much is lost is to compute the percentage loss: S", \I(x) – O(x)*dx S", \I(x)|²dx A = where O(x) represents the output signal, also defined for x E [-n, 7]. For example, suppose we are given a transistor that sends an input I(x) to 1 O(2) = | 1(0)dt +(" () sin(t)dt) sin(2). (a) What is the percentage loss if the input and output are equal? What is the percentage loss if the output is zero (i.e. O(x) = 0 for all x E [–T,7])? (b) Suppose Mr. MacGyver tries several experiments to…