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EXERCISE 9.2

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EXERCISE 9.2 1.     Thus is strictly decreasing. 2.         Thus is strictly increasing. 3.             Thus is strictly increasing. 4.         Thus is strictly decreasing 5.     Thus is strictly decreasing. 6.         Thus is strictly decreasing. Loading… … Read more

EXERCISE 9.1

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EXERCISE 9.1 1. (a)     (b)     (c)     (d)     2. (a)         Then \quad for . And         (b)     and     3. (a)     (b)     (c)         and     4.     (b) … Read more

EXERCISE 7.4

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  EXERCISE 7.4 Evaluate the integral. (1)         Let         then (1) becomes     Since Then the  last integral takes the form         From (2) we have     Since     Substituting (4)-(6) into (3)     (2)     Then (1) becomes   … Read more

EXERCISE 7.3

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Calculus exercise 7.3

  Exercise 7.3 Evaluate the integral. (1)         then (1) becomes     From (2) substituting into (3).     (2)     then (1) becomes     From (2) substituting into (3)       (3)     We know that     then (1) becomes     (4)     … Read more

EXERCISE 7.2

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Calculus exercise 7.2

Integration by parts technique is used to solve problems in a simple way with complete steps. Evaluate the integral.     Integrating by parts     Here     2.     Here     Formula integration by parts:     integrating by parts     3.     Integrating by parts     Again … Read more

EXERCISE 7.1

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Calculus exercise 7.1

  1-30 Evaluate the integrals by making appropriate u-substitution.     Let         then (1) be comes     Integrating w.r.t , we get             2.         then (1) becomes         From (2) Substituting into (3), we get     3.  … Read more