Calculus II PLTL Fall 2014 Worksheet 7 These problems are to be done without the use of a calculator unless otherwise specified R 1 Round Robin Use a substitution to change the integral cos 1 x x dx into one you can find in the integral table in your text Then evaluate it 2 Scribe Evaluate R 2 0 2 sinh sin cos d R1 3 Pairs Evaluate the integral 03 6 1 9x2 dx three different ways a Make the substitution u 3x and then use an integral table to express the integral in terms of a hyberbolic trigonometric function b Make the substitution u 3x and then use the correspondence between hyperbolic trig functions and natural logarithms to express the integral in terms of natural logs c Make the trigonometric substitution tan 3x and solve 4 Scribe Find a parametrization defining the movement of a particle moving as described below a The particle starts at the point 1 3 and moves in a straight line to the point 3 2 b The particle starts at 1 2 and moves counterclockwise around the circle x2 y 1 2 4 5 Pairs Consider the function f x xe x R1 a Evaluate the definite integral 0 f x dx R 10 b Evaluate the definite integral 0 f x dx R 100 c Evaluate the definite integral 0 f x dx R d Evaluate the improper integral 0 f x dx if it is convergent or explain why it is divergent 6 Round Robin Calculate the derivative with respect to x of each of the functions below x 0 a f x ln x 1 b f x 2 ln x 1 c f x x 1 1 d f x x 1 2 e f x ln x 1 x 1 1 f f x ln x 1 x 1 1 g f x 2 ln x 1 x 1 1 h f x 2 ln x 1 x 1 1 i f x ln x 1 x 1 2 j f x ln x 1 x 1 2 How could you use the work you just did to answer the following question R With partial fractions you get x 2 x2 2x 1 dx f x C What is f x
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