MATHEMATICS-MULTIPLE INTERGRATION QUESTIONS AND
ANSWERS, A+ GURANTEED.
1
Q
Volume between two equal regions between 3d curvatures
A
Volume is equal to the double integral of the multivariable function
V=∫∫(g(x,y)-f(x,y))dA
2
Q
Average value of a 3d surface function within a given region
A
(∫∫f(x,y)dA)/(RegionArea)
3
Q
Volume for a non rectangular regions
A
∫∫ f(x,y)
set second interval from one function value to another
4
Q
Volumes of additional regions
A
, Always the sum
∫∫total(x)=∫∫f1(x)+∫∫f2(x)
Applies for triple integrals too
5
Q
Area within a polar curve section
A
∫∫f(r,θ)=∫∫f(r,θ) r dr dθ
First interval- largest angle, smallest angle
Second Interval- larger radius, smaller radius
6
Q
Area between two polar functions
A
∫∫f(r,θ)=∫∫f(r,θ) r dr dθ
First interval- largest angle, smallest angle
Second Interval- greater function, smaller function
7
Q
Volume under a function of three variables
A
∫∫∫f(x,y,z)dV
First Interval- b,a (region within the x-coordinate)
Second Interval- upper function on xy-axis, lower curve on xy-axis (describes the region)
Third Interval- upper function on 3d-axis, lower surface on 3d-axis (describes the surfaces)
8
ANSWERS, A+ GURANTEED.
1
Q
Volume between two equal regions between 3d curvatures
A
Volume is equal to the double integral of the multivariable function
V=∫∫(g(x,y)-f(x,y))dA
2
Q
Average value of a 3d surface function within a given region
A
(∫∫f(x,y)dA)/(RegionArea)
3
Q
Volume for a non rectangular regions
A
∫∫ f(x,y)
set second interval from one function value to another
4
Q
Volumes of additional regions
A
, Always the sum
∫∫total(x)=∫∫f1(x)+∫∫f2(x)
Applies for triple integrals too
5
Q
Area within a polar curve section
A
∫∫f(r,θ)=∫∫f(r,θ) r dr dθ
First interval- largest angle, smallest angle
Second Interval- larger radius, smaller radius
6
Q
Area between two polar functions
A
∫∫f(r,θ)=∫∫f(r,θ) r dr dθ
First interval- largest angle, smallest angle
Second Interval- greater function, smaller function
7
Q
Volume under a function of three variables
A
∫∫∫f(x,y,z)dV
First Interval- b,a (region within the x-coordinate)
Second Interval- upper function on xy-axis, lower curve on xy-axis (describes the region)
Third Interval- upper function on 3d-axis, lower surface on 3d-axis (describes the surfaces)
8
