Chap5_Sec2

Chap5_Sec2 - x =(2 1/5 = 1/5 s So the Midpoint Rule gives 2...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon
EVALUATING INTEGRALS Evaluate the following integrals by interpreting each in terms of areas. a. b. 1 2 0 1 x dx - 3 0 ( 1) x dx - Example 4 (5.2)
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
EVALUATING INTEGRALS Since y 2 = 1 - x 2 , we get: x 2 + y 2 = 1 s This shows that the graph of f is the quarter-circle with radius 1. Example 4 a 1 2 2 1 4 0 1 (1) 4 x dx π - = = Since we can interpret this integral as the area under the curve from 0 to 1. 2 ( ) 1 0 f x x = - 2 1 y x = -
Background image of page 2
EVALUATING INTEGRALS The graph of y = x – 1 is the line with slope 1 shown here. s We compute the integral as the difference of the areas of the two triangles: 3 1 1 1 2 2 2 0 ( 1) (2 2) (1 1) 1.5 x dx A A - = - = - = Example 4 b
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
MIDPOINT RULE Use the Midpoint Rule with n = 5 to approximate s The endpoints of the five subintervals are: 1, 1.2, 1.4, 1.6, 1.8, 2.0 s So, the midpoints are: 1.1, 1.3, 1.5, 1.7, 1.9 s The width of the subintervals is:
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 6
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: x = (2 - 1)/5 = 1/5 s So, the Midpoint Rule gives: 2 1 1 dx x ∫ Example 5 (5.2) [ ] 2 1 1 (1.1) (1.3) (1.5) (1.7) (1.9) 1 1 1 1 1 1 5 1.1 1.3 1.5 1.7 1.9 0.691908 dx x f f f f f x ≈ Δ + + + + = + + + + ≈ ∫ MIDPOINT RULE As f ( x ) = 1/ x for 1 ≤ x ≤ 2, the integral represents an area, and the approximation given by the rule is the sum of the areas of the rectangles shown. Example 5 PROPERTIES OF INTEGRALS If it is known that find: 10 8 ( ) 17 and ( ) 12 f x dx f x dx = = ∫ ∫ Example 7 (5.2) 10 8 ( ) f x dx ∫ 8 10 10 8 ( ) ( ) ( ) f x dx f x dx f x dx + = ∫ ∫ ∫ 10 10 8 8 ( ) ( ) ( ) 17 12 5 f x dx f x dx f x dx =-=-= ∫ ∫ ∫...
View Full Document

This note was uploaded on 05/23/2011 for the course MAC 2311 taught by Professor Noohi during the Fall '08 term at FSU.

Page1 / 6

Chap5_Sec2 - x =(2 1/5 = 1/5 s So the Midpoint Rule gives 2...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online