quiz 9

Question 1

bit of circle parameterization for line integrals

Answer 1

x = acos(t)
y=asin(t)
ds=adt. a ∈ R

Question 2

bit of graph parameterization for line integrals

Answer 2

x=t
y=g(t) *the function
a≤t≤b
ds = sqrt(1+(g’(t))^2) dt

Question 3

bit of line/vector parameterization for line integrals

Answer 3

Let <a,b> and <c,d> be vectors
x=a+(c-a)t
y=b+(d-b)t
0≤t≤1 Always
ds = sqrt((c-a)^2 + (d-b)^2) dt

Question 4

bit of graph parameterization for surface integrals

Answer 4

x=x
y=y
z=g(x,y)
η=<g_x,g_y,-1>
dS=sqrt((g_x)^2 + (g_y)^2 +1)dA (bounds are x and y)

Question 5

bit of cylinder parameterization for surface integrals

Answer 5

x^2 + y^2 = a^2
x= acos theta
y= asin theta
z = z
η = <acosθ, asinθ, 0>
dS = a*dA (bounds are z and θ)