Let R be the region to the right of y = x² below y = -2x + 80 and above y = 2x + 48. You can see this region in the following graph. 182 34 (a) These curves intersect at (x, y) = (-10, 100), (-6,36), ( (Give your answer as a comma separated list, for example: (a,b), (c,d) ...) (b) If we use vertical slices for this area, we get where A = = [° f (x) dr + √ g(x)dx a= -10 b= -6 , C= 8 , f(x) = -2x+80-(x^2) , g(x) = -2x+80-(2x+48) (c) If we use horizontal slices for this area, we get e 1 = [ h(y) n(y) dy + ['j A j(y) dy where d= 36 , e= 64 , f= 100 , h(y) = ((1/2)y-24)-(sqrt(y)) , j(y) = (d) In both cases, we get that the area is A = 1544/3
Let R be the region to the right of y = x² below y = -2x + 80 and above y = 2x + 48. You can see this region in the following graph. 182 34 (a) These curves intersect at (x, y) = (-10, 100), (-6,36), ( (Give your answer as a comma separated list, for example: (a,b), (c,d) ...) (b) If we use vertical slices for this area, we get where A = = [° f (x) dr + √ g(x)dx a= -10 b= -6 , C= 8 , f(x) = -2x+80-(x^2) , g(x) = -2x+80-(2x+48) (c) If we use horizontal slices for this area, we get e 1 = [ h(y) n(y) dy + ['j A j(y) dy where d= 36 , e= 64 , f= 100 , h(y) = ((1/2)y-24)-(sqrt(y)) , j(y) = (d) In both cases, we get that the area is A = 1544/3
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:Let R be the region to the right of y = x² below y = -2x + 80 and above y = 2x + 48.
You can see this region in the following graph.
182
34
(a) These curves intersect at (x, y) = (-10, 100), (-6,36), (
(Give your answer as a comma separated list, for example: (a,b), (c,d) ...)
(b) If we use vertical slices for this area, we get
where
A =
= [° f (x) dr + √
g(x)dx
a= -10
b= -6
, C= 8
, f(x) = -2x+80-(x^2)
, g(x) =
-2x+80-(2x+48)
(c) If we use horizontal slices for this area, we get
e
1 = [ h(y)
n(y) dy + ['j
A
j(y) dy
where
d= 36
, e= 64
, f= 100
, h(y) = ((1/2)y-24)-(sqrt(y))
, j(y) =
(d) In both cases, we get that the area is A = 1544/3
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