
Integration in Mathematics II Second Semester
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.
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Presentation Transcript
MATHEMATICSII SECONDSEMESTER 05 INTEGRATION Dr. Shaimaa Amen / 1st year/ Material engineering department 2020-2021
Outlines Indefinite Integral Basic Integration Formulas The Substitution Rule The Integrals of Sin2x and Cos2x
Indefinite Integrals and the SubstitutionRule EXAMPLE1: Evaluate Solution:
7. 8. 9. 10. 11. 12. 13.
The Substitution Rule Substitution: Running the Chain Rule Backwards
EXAMPLE EXAMPLE2 2: Adjusting the Integrand by a Constant
EXAMPLE EXAMPLE3 3: UsingSubstitution EXAMPLE4: UsingSubstitution
EXAMPLE EXAMPLE6: 6: Using Different Substitutions, Evaluate
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.