Indefinite Integration Questions and Answers

The function is defined on the closed interval 3 8 and is g graph above Let g be the function defined by g x 71 t de a Find g 3 and g 0 b Does g x have a relat the interval s are g x is concave down Give a reas 1 x 3020 d Find sin 2x Wr Evaluate the following expressions t to the p x x 1 Explain your reason 3x sin 3t 1 dt In 4t dt

2 Determine if the integral is convergent or divergent dx If the integral is convergent evaluate x the integral

Find the indefinite integral using substitution for 10z 52 2 10x 272 C 5x 4 C 5 4 10x 5x 4 C

2 2 Ex 5y 1 We consider equation E xyEN We Suppose that xy is d caple solutias of the equation E parity 1 Can x and y have the some 2 KEN copy and complete the tablet 6 E 5 1 2 3 4 4 5 3 Deduce x 1 5 or x 4 5 4 Find a non triviale solution different from 1 0

1 10 points What is the maximum vertical distance between the parabola y x 2 1 and the line y 2x 5 6 d 4 yz x 2 1 2x 5 y 2 x 2 2 2x 4 2 2x 6 3 y 2 max vertical distance 0

If log 2 0 4307 and log 3 0 6827 then using the product and power properties of logarithms what is the approximate value of log 6 Your final answer must be accurate to three places after the b decimal

5 f x on 3 5 x 2

From the 2013 IPE AB5 a Find g 6 and g 3 6 4 5 4 M 6 Graph of f 12 The graph of the continuous function f consisting of three line segments and a semicircle is shown above Let g be the function given by g x L f t dt b Find g 0 4 3 2 c Find all values of x on the open interval 6 x 3 for which the graph of g has a horizontal tangent Determine whether g has a local maximum a local minimum or neither at each of these values Justify your answers d Find all values of x on the open interval 6 x 3 for which the graph of g has a point of inflection Explain your reasoning

What is the slope of the line with the equation y 3x 2 a 0 c 1 b 3 d 5

4 A function f t gives the rate of evaporation of water in liters per hour from a pond where t is measured in f t dt in the context described 10 hours since 12 noon Which of the following gives the meaning of A The total volume of water in liters that evaporated from the pond during the first 10 hours after 12 noon B The total volume of water in liters that evaporated from the pond between 4PM and 10PM C The net change in the rate of evaporation in liters per hour from the pond between 4PM and 10PM D The average rate of evaporation in liters per hour from the pond between 4PM and 10PM E The average rate of of change in the rate of evaporation in liters per hour per hour from the pond between 4PM and 10PM