Exploring Properties of Definite Integrals in Mathematics II Second Semester

Delve into the world of definite integrals in Mathematics II Second Semester, understanding rules, properties, and applications through examples. Learn to find bounds, evaluate integrals, calculate areas under curves, and graph functions for a comprehensive understanding of this mathematical concept.

• Mathematics
• Definite Integrals
• Properties
• Rules
• Applications

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1. MATHEMATICSII SECONDSEMESTER 06 The Definite Integral

2. TheDefiniteIntegral

3. PropertiesofDefiniteIntegrals When andg are integrable on the interval [a , b], the definite integral satisfies Rules 1 to7 in Table5.3.

5. Usingthe Rules for Definite Integrals,Supposethat. EXAMPLE1:

6. EXAMPLE2: Finding Bounds for anIntegral Show that the value of is less than 3\2

7. AreaUnderaCurveasaDefiniteIntegral

9. In conclusion, we have the following rule for integratingf(x)= x. This formulagivesthe areaof a trapezoid down tothe line y= x(seeFigure).

10. EXAMPLE4: on[-2,2]. Solution :

11. EXAMPEL5:

12. EXERCISES5.3 1. UsingPropertiesand KnownValuestoFind Other Integrals. A. B.

13. 2. Use the rules in Table5.3 and Equations (1) to evaluate the integralsin Exercises41 50. 3. In Exercises 51 54 use a definite integral to find the area of the region between the given curve and the x-axison the interval [0, b].

14. 4. In Exercises5562,graph the functionand find its averagevalue over the given interval. 5. Theory and Examples