1 c Kathryn Bollinger November 12 2010 Week In Review 9 5 3 5 4 5 5 1 Integrate the following 1 2x 3 e 2 e2 x a Z b Z c Z y 1 4 5y 3 2 10y dy d Z csc2 x ex e Z x 3 1 3 t4 t dt 6t t 2 dt 5 x7 dx dx 2 c Kathryn Bollinger November 12 2010 f Z g Z h Z 5z 4 6z 2 z3 p dz 3x2 x3 6 dx 8ye 2y 2 3 dy 3 c Kathryn Bollinger November 12 2010 i Z x 2 2 2x 8x 6 j Z 1 x ln x k Z h dx i t t 8 100 dt dx 4 c Kathryn Bollinger November 12 2010 l Z m Z e2y e2y 3 4 tan x dx dy 5 c Kathryn Bollinger November 12 2010 2 Evaluate the following EXACTLY a Z b x3 a b Z 4 Z 2 Z 3 1 x dx et dt 2 c 2 cos x 6 dx 0 d 1 x2 1 x3 3x dx 0 a b 6 c Kathryn Bollinger November 12 2010 3 Is Z 1 2 1 x2 x 1 dx 1 1 2 1 3 1 correct Why or why not 2 2 4 If n t gives the rate of change of the population of College Station in thousands of people per year what does Z 4 n t dt represent if t 0 corresponds to 2010 2 5 A certain weed grows at the rate of g t 0 5e0 1t cm day If the weed is 6 cm tall after 2 days how tall is the weed after t days 6 The rate of change of sales of a brand new soup in thousands per month is given by R t t 2 where t is the time in months that the new product has been on the market Find the total sales after 9 months given that there will be no sales of the soup before it hits the market c Kathryn Bollinger November 12 2010 7 7 A particle moves along a line with velocity function v t t2 4t where v is measured in meters per second Find a The displacement of the particle during the first 10 seconds b The distance traveled by the particle during the first 10 seconds 8 c Kathryn Bollinger November 12 2010 8 Let g x Z x f t dt where f is the function whose graph is shown 0 4 2 2 6 a Evaluate g 0 g 4 and g 6 b On what interval s is g increasing Decreasing c Where does g have an absolute maximum value Absolute minimum value 9 c Kathryn Bollinger November 12 2010 9 Use Part I of the Fundamental Theorem of Calculus to find the derivative of each of the following functions a g x Z 2 Z ln x ln t4 6t dt x b h x c f x Z p 3 v 2 8 dv 1 x4 x2 e3y 2 8 dy 10 c Kathryn Bollinger November 12 2010 10 Use properties of integrals and their relationship to area in order to evaluate Z b x x dx b
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