PostClass 7.4-solutions

1 to determine a set x 1 then a 1 4 on the other

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: in which case graph of g 1 = A(x + 3) + B (x − 1) . 1 To determine A, set x = 1. Then A= 1 . 4 On the other hand, to determine B , set x = −3. Then 1 B=− . 4 Thus I= 1 1 dx − x−1 4 1 4 1 dx . x+3 graph of f −3 3 (axes not drawn to scale). To express the area as a definite integral we need to find where the graphs intersect, i.e. when 7 = 1. 16 − x2 Consequently, I= 1 ln 4 x−1 x+3 +C Thus the graphs intersect when x = ±3. Hence 3 Area = with C an arbitrary constant. 007 f ( x) = 7 , 16 − x2 1. Area = 3 − g ( x) = 1 . 77 sq.units ln 82 2. Area = 3 − 7 ln 7 sq.units 4 3. Area = 6 − 7 ln 7 sq.units correct 4 4. Area = 3 + 3 10.0 points Find the bounded area enclosed by the graphs of f and g when 7 ln 7 sq.units 8 (g (x) − f (x)) dx −3 =2 1− 0 7 dx 16 − x2 since both f and g are even functions. To evaluate this integral we must first use partial fractions: 7 7 = 2 16 − x (4 − x)(4 + x) = 7 1 1 . + 8 4−x 4+x Thus the area is gi...
View Full Document

This homework help was uploaded on 03/21/2014 for the course M 408S taught by Professor Stepp during the Spring '11 term at University of Texas at Austin.

Ask a homework question - tutors are online