Multivariable Calculus - Double Integrals

運算式 17: left bracket, "y" Subscript, 1 , Baseline less than "y" less than "y" Subscript, 2 , Baseline , right bracket

運算式 18: "y" Subscript, 1 , Baseline equals negative 4

negative "R" Subscript, "a" "d" "i" "u" "s" , Baseline

"R" Subscript, "a" "d" "i" "u" "s" , Baseline

運算式 19: "y" Subscript, 2 , Baseline equals 4

negative "R" Subscript, "a" "d" "i" "u" "s" , Baseline

"R" Subscript, "a" "d" "i" "u" "s" , Baseline

Calculation Method

運算式 21: "M" Subscript, "e" "t" "h" "o" "d" , Baseline equals 0

Method = 0 for the definite integral (volume under z = 0 is counted as negative) Method = 1 for volume under the surface (volume under z = 0 is counted as positive)

Calculations

"V" "o" "l" "u" "m" "e"	"V" Subscript, "o" "l" "u" "m" "e" , Baseline
r1c1:	r1c2: 136.9 5 2 9 4	r1c3:
r2c1:	r2c2:	r2c3:

"S" "u" "r" "f" "a" "c" "e" "A" "r" "e" "a"	"S" Subscript, "u" "r" "f" "a" "c" "e" "A" "r" "e" "a" , Baseline
r1c1:	r1c2: 68.3 9 8 6 1 4	r1c3:
r2c1:	r2c2:	r2c3:

Formulas

運算式 27: "V" "o" "l" "u" "m" "e" equals Start integral from "y" Subscript, 1 , Baseline to "y" Subscript, 2 , Baseline , end integral, Start integral from "x" Subscript, 1 , Baseline to "x" Subscript, 2 , Baseline , end integral, "f" left parenthesis, "x" , "y" , right parenthesis "d" "x" "d" "y"

新增滑桿：

運算式 28: "S" "u" "r" "f" "a" "c" "e" "A" "r" "e" "a" equals Start integral from "y" Subscript, 1 , Baseline to "y" Subscript, 2 , Baseline , end integral, Start integral from "x" Subscript, 1 , Baseline to "x" Subscript, 2 , Baseline , end integral, StartRoot, StartFraction, ∂ "f" Over ∂ "x" , EndFraction left parenthesis, "x" , "y" , right parenthesis squared positive StartFraction, ∂ "f" Over ∂ "y" , EndFraction left parenthesis, "x" , "y" , right parenthesis squared positive 1 , EndRoot "d" "x" "d" "y"

Perspective View

運算式 30: theta Subscript, "h" "o" "r" "i" "z" "o" "n" "t" "a" "l" , Baseline equals negative 0.5

negative pi

運算式 31: theta Subscript, "v" "e" "r" "t" "i" "c" "a" "l" , Baseline equals negative 0.4 5

negative pi

運算式 32: theta Subscript, "c" "i" "r" "c" "u" "l" "a" "r" , Baseline equals 0

negative pi

Visual Representation Construction

108

技術支援

"x"

"y"

"z"

Perspective

"x" Subscript, 1 , Baseline equals negative 4

"x" Subscript, 2 , Baseline equals 4

"y" Subscript, 1 , Baseline equals negative 4

"y" Subscript, 2 , Baseline equals 4

Statistics

"S" "u" "r" "f" "a" "c" "e" "A" "r" "e" "a" equals Start integral from "y" Subscript, 1 , Baseline to "y" Subscript, 2 , Baseline , end integral, Start integral from "x" Subscript, 1 , Baseline to "x" Subscript, 2 , Baseline , end integral, StartRoot, StartFraction, ∂ "f" Over ∂ "x" , EndFraction left parenthesis, "x" , "y" , right parenthesis squared positive StartFraction, ∂ "f" Over ∂ "y" , EndFraction left parenthesis, "x" , "y" , right parenthesis squared positive 1 , EndRoot "d" "x" "d" "y" equals 68.4

"V" "o" "l" "u" "m" "e" equals Start integral from "y" Subscript, 1 , Baseline to "y" Subscript, 2 , Baseline , end integral, Start integral from "x" Subscript, 1 , Baseline to "x" Subscript, 2 , Baseline , end integral, "f" left parenthesis, "x" , "y" , right parenthesis "d" "x" "d" "y" equals 137