Integration in Mathematics II Second Semester

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Explore the fundamentals of integration, including basic formulas, the substitution rule, and examples in indefinite integrals. Dive into various techniques and exercises to enhance your understanding of integration in the second semester of Mathematics II for Material Engineering students in the academic year 2020-2021.

  • Mathematics
  • Integration
  • Formulas
  • Substitution Rule
  • Material Engineering

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  1. MATHEMATICSII SECONDSEMESTER 05 INTEGRATION Dr. Shaimaa Amen / 1st year/ Material engineering department 2020-2021

  2. Outlines Indefinite Integral Basic Integration Formulas The Substitution Rule The Integrals of Sin2x and Cos2x

  3. Indefinite Integrals and the SubstitutionRule EXAMPLE1: Evaluate Solution:

  4. 7. 8. 9. 10. 11. 12. 13.

  5. The Substitution Rule Substitution: Running the Chain Rule Backwards

  6. EXAMPLE1: Using the PowerRule

  7. EXAMPLE EXAMPLE2 2: Adjusting the Integrand by a Constant

  8. EXAMPLE EXAMPLE3 3: UsingSubstitution EXAMPLE4: UsingSubstitution

  9. EXAMPLE5: Using Identities andSubstitution

  10. EXAMPLE EXAMPLE6: 6: Using Different Substitutions, Evaluate

  11. EXERCISES EXERCISES5 5 1. Evaluate the indefinite integrals in Exercises 1 12 by using the given substitutions to reduce the integrals to standardform. 2. Evaluate the integrals in Exercises13 48.

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