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Lecture

7.7 Approximate Integration Question #3 (Medium)

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Department
Mathematics
Course
MAT136H1
Professor
All Professors
Semester
Winter

Description
7.7 Integral Techniques Integral Approximation Question #3 (Medium): Computing the Error Bounds Sample Question Find the approximation , , and for . Then compute the corresponding errors , , and (answers rounded to 6 decimal places). What observations can you make? And what happens when is doubled? ∫ Solution First evaluate the integral: ∫ * + * + * + Now approximation calculations: For and interval [ ], . The intervals are: * + * + * + * +. Midpoint: ∑ [ ( ̅ ] * ( ) ( ) ( ) ( )+ [ ( ) ( ) ] . Trapezoidal: [ ( ) ( ) ( ) ( )] [ ( ) ( ) ( ) ( ) ( ) ] [ ] . Simpson’s: [ ( ) ( ) ( ) ( ) ( ) ] ( ) [ ] [ ] . Then the error bounds: ∫ ( ) ( ) ( ) ( ) ; ; For and interval [ ],
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