Integration By U Substitution Worksheet In this unit we will meet several examples of integrals where it is appropriate to make a substitution In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature 3 Finding Z 1 Introduction
Calculus 1 Tutor Worksheet 11 Integration by Substitution 1 Evaluate the integral using substitution t t y 5 2 Evaluate the integral using substitution sin t 3 Evaluate the integral using substitution w w u Evaluate each indefinite integral Use the provided substitution 1 15 x4 3x5 1 5 dx u 3x5 1 2 16 x3 4x4 1 5 dx u 4x4 1 3 8x3 2x4 5 5 dx u 2x4 5 4 5x4 5 2 3 20 x3 dx u 5x4 5 5 5 ln x 5 x dx u 5 ln x 6 4sec 4x tan 4x sec 4 4xdx u sec
Integration By U Substitution Worksheet
Integration By U Substitution Worksheet
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Quiz Worksheet U Substitution Study
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Integration By U Substitution Example Problem 3 YouTube
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U Substitution Recall the substitution rule from MATH 141 see page 241 in the textbook Theorem If u g x is a di erentiable function whose range is an interval I and f is continuous on I then f g x g x dx f u du This method of integration is helpful in reversing the chain rule Can you see why Let s look at some Integration Worksheet Substitution Method Solutions a Let u 4x 5 b Then du 4 dxor 1 4 du dx c Now substitute Z p 4x 5 dx Z u 1 4 du Z 1 4 u1 2 du 1 4 u3 2 2 3 C 1
Math 229 Integration Worksheet Substitution Method Integrate 1 Z 5x 4 5 dx 2 Z 3t2 t3 4 5 dt 3 Z p 4x5dx 4 Z t2 t3 4 1 2 dt 5 Z cos 2x 1 dx 6 Z sin10 xcosxdx 7 Z sinx cosx 5 dx 8 Z p x1 2 p x dx 9 Z p Express each definite integral in terms of u but do not evaluate 1 1 0 8x 4x 2 1 dx u 4x2 1 2 0 1 12 x2 4x3 1 3 dx u 4x3 1 3 1 2 6x x 2 1 dx u x2 1 4 0 1 24 x 4x 2 4 dx u 4x2 4 Evaluate each definite integral 5
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Integration by Substitution Date Period Evaluate each indefinite integral Use the provided substitution 1 20 x3 25 25 x8 dx u 5x4 sin 1 5x4 5 C 2 10 x4 9 4x10 dx u 2x5 1 3 tan 1 2x5 3 C 3 2 csc 2 2x cot 2x cot 2 2x 1 dx u cot 2x sec 1 cot 2x C 4 1 x 25 ln U substitution is the first integration technique that should be considered before pursuing the implementation of a more advanced approach This technique which is analogous to the chain rule of differentiation is useful whenever a function
On this worksheet you will use substitution as well as the other integration rules to evaluate the the given de nite and inde nite integrals Steps for integration by Substitution 1 Determine u think parentheses and denominators 2 Find du dx 3 Rearrange du dx until you can make a substitution 4 Make the substitution to obtain an integral in u Created by T Madas Created by T Madas Question 3 Carry out the following integrations by substitution only 1 3 5 4 2 3 10 5 3 5 3 5 3 25 10 x x dx x x C 2 12 3 2 1 3ln 2 1 2 1 x
New Doc 2017 08 31 Cal 2 Math 181 Worksheet Chapter 3 Integration By
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U substitution With Definite Integrals YouTube
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Integration By U Substitution Worksheet - U Substitution Recall the substitution rule from MATH 141 see page 241 in the textbook Theorem If u g x is a di erentiable function whose range is an interval I and f is continuous on I then f g x g x dx f u du This method of integration is helpful in reversing the chain rule Can you see why Let s look at some