Review of Accumulation and Rates he integral of a rate of change gives the net change....

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Review of Accumulation and Rates he integral of a rate of change gives the net change. The general form of the equation is ] (x) = f(x)+ f'(1)dt, x = x, is the initial time, and f(x) is the initial value. Xo Since this is one of the main interpretations of the definite integral the concept may come up in a variety of situations. What you should know how to do: Understand the equation. It is often not necessary to do as much computation as it seems at first. The FTC may help differentiating F. Often these problems contain a lot of writing; be ready to read and apply. Explain the meaning of a derivative or definite integral or its value in terms of the context of the problem. In-out problems: 2 rates of change work together but in opposite directions. Max/min and inc/dec analysis. Explain the meaning of a definite integral in context. The explanation should include (1) what the integral gives, (2) the units and (3) an accounting of the limits of integration. 1. Consider G(x) = [In (1+1) di . 2 a. G(x) has an x-intercept at x= b. For what values of x is G(x) <0. x c. In general, how does the graph of G(x) compare to F(x)=In(t+1)dt? Use your properties of integrals to help you answer this question. T {f(1)de. 3. Let h(x)=5+ (1)dt. a. State the domain for h. b. Find h(0). c. h'(0). d. On what intervals is h(x) decreasing? Justify your answer. e. On what intervals is h(x) concave down? Justify your answer. Review of Accumulation and Rates he integral of a rate of change gives the net change. The general form of the equation is ] (x) = f(x)+ f'(1)dt, x = x, is the initial time, and f(x) is the initial value. Xo Since this is one of the main interpretations of the definite integral the concept may come up in a variety of situations. What you should know how to do: Understand the equation. It is often not necessary to do as much computation as it seems at first. The FTC may help differentiating F. Often these problems contain a lot of writing; be ready to read and apply. Explain the meaning of a derivative or definite integral or its value in terms of the context of the problem. In-out problems: 2 rates of change work together but in opposite directions. Max/min and inc/dec analysis. Explain the meaning of a definite integral in context. The explanation should include (1) what the integral gives, (2) the units and (3) an accounting of the limits of integration. 1. Consider G(x) = [In (1+1) di . 2 a. G(x) has an x-intercept at x= b. For what values of x is G(x) <0. x c. In general, how does the graph of G(x) compare to F(x)=In(t+1)dt? Use your properties of integrals to help you answer this question. T {f(1)de. 3. Let h(x)=5+ (1)dt. a. State the domain for h. b. Find h(0). c. h'(0). d. On what intervals is h(x) decreasing? Justify your answer. e. On what intervals is h(x) concave down? Justify your answer.