PWWWW.ma tudent/PlayerHomework.aspx?homeworkld Math 148-Calculus 1- Spring 2018
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Question
PWWWW.ma tudent/PlayerHomework.aspx?homeworkld Math 148-Calculus 1- Spring 2018 Homework: Section 7.3 Score: 0 of 1 pt 7.3.11 2 of 3 (0 comple Approximate the area under the graph of f(x) and above the x-axis with rectangles, using the following methods with n 4 (a) Use left endpoints. (b) Use right endpoints. (c) Average the answers in parts (a) and (b) (d) Use midpoints i(x) + 4, from x to x The area, approximated using the left endpoints, is (Round to two decimal places as needed.) Enter your answer in the answer box and then click Check Answer.Explanation / Answer
Given
f(x) = 3/x + 4
n = 4 , x = a = 1 to x = b = 9
delta x = ( b - a ) / n
= ( 9 - 1 ) / 4
= 8 / 4
= 2
delta x = 2
divide interval into sub intervals [ 1, 9 ]
[ 1, 3 ] , [ 3, 5 ] , [ 5, 7 ] , [ 7 , 9 ]
( a ) use left end points
L4 = delta x [ f(1) + f(3) + f(5) + f(7) ]
= 2 [ ( 3/1+4) + ( 3/3+4) + ( 3/5+4) + ( 3/7+4) ]
= 2 [ 7 + 5 + ( 23/5) + ( 31/7) ]
= 42.05714285
( b ) Use Right End points
R4 = delta x [ f(3) + f(5) + f(7) + f(9) ]
= 2 [ ( 3/3+4) + ( 3/5+4) + ( 3/7+4) + ( 3/9 + 4 ) ]
= 2 [ 5 + 23/5 + 31/7 + 13/3 ]
= 36.723809523
( c )
Average A = ( L4 + R4 ) /2
= ( 42.05714285 + 36.723809523 ) / 2
A = 39.390476186
( d ) midpoints
intervals
[ 1,3] = ( 1 + 3 )/2 => 2
[ 3,5] = ( 3 + 5) /2 => 4
[ 5,7] = (5 + 7) /2 => 6
[ 7,9] = ( 7 + 9) /2 => 8
M4 = delta x [ f(2 ) + f(4) + f(6) + f(8) ]
= 2 [ ( 3/2 + 4) + ( 3/4 + 4 ) + (3/6 + 4 ) + ( 3/8 + 4 ) ]
= 2 [ 11/2 + 19/4 + 9/2 + 35/8 ]
= 38.25
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